url
stringclasses 147
values | commit
stringclasses 147
values | file_path
stringlengths 7
101
| full_name
stringlengths 1
94
| start
stringlengths 6
10
| end
stringlengths 6
11
| tactic
stringlengths 1
11.2k
| state_before
stringlengths 3
2.09M
| state_after
stringlengths 6
2.09M
|
|---|---|---|---|---|---|---|---|---|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | case _ right =>
apply Exists.elim right
intro zs a2
apply Exists.intro zs
tauto | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
right : β ys, y β ys β§ (hd.1, ys) β tl
β’ β ys, y β ys β§ ((hd.1, ys) = hd β¨ (hd.1, ys) β tl) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | apply Exists.intro hd.snd | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
left : y β hd.2
β’ β ys, y β ys β§ ((hd.1, ys) = hd β¨ (hd.1, ys) β tl) | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
left : y β hd.2
β’ y β hd.2 β§ ((hd.1, hd.2) = hd β¨ (hd.1, hd.2) β tl) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | tauto | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
left : y β hd.2
β’ y β hd.2 β§ ((hd.1, hd.2) = hd β¨ (hd.1, hd.2) β tl) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | apply Exists.elim right | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
right : β ys, y β ys β§ (hd.1, ys) β tl
β’ β ys, y β ys β§ ((hd.1, ys) = hd β¨ (hd.1, ys) β tl) | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
right : β ys, y β ys β§ (hd.1, ys) β tl
β’ β (a : List Node), y β a β§ (hd.1, a) β tl β β ys, y β ys β§ ((hd.1, ys) = hd β¨ (hd.1, ys) β tl) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | intro zs a2 | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
right : β ys, y β ys β§ (hd.1, ys) β tl
β’ β (a : List Node), y β a β§ (hd.1, a) β tl β β ys, y β ys β§ ((hd.1, ys) = hd β¨ (hd.1, ys) β tl) | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
right : β ys, y β ys β§ (hd.1, ys) β tl
zs : List Node
a2 : y β zs β§ (hd.1, zs) β tl
β’ β ys, y β ys β§ ((hd.1, ys) = hd β¨ (hd.1, ys) β tl) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | apply Exists.intro zs | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
right : β ys, y β ys β§ (hd.1, ys) β tl
zs : List Node
a2 : y β zs β§ (hd.1, zs) β tl
β’ β ys, y β ys β§ ((hd.1, ys) = hd β¨ (hd.1, ys) β tl) | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
right : β ys, y β ys β§ (hd.1, ys) β tl
zs : List Node
a2 : y β zs β§ (hd.1, zs) β tl
β’ y β zs β§ ((hd.1, zs) = hd β¨ (hd.1, zs) β tl) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | tauto | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
right : β ys, y β ys β§ (hd.1, ys) β tl
zs : List Node
a2 : y β zs β§ (hd.1, zs) β tl
β’ y β zs β§ ((hd.1, zs) = hd β¨ (hd.1, zs) β tl) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | intro a1 | case mpr
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
β’ (β ys, y β ys β§ ((hd.1, ys) = hd β¨ (hd.1, ys) β tl)) β y β hd.2 β¨ β ys, y β ys β§ (hd.1, ys) β tl | case mpr
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
a1 : β ys, y β ys β§ ((hd.1, ys) = hd β¨ (hd.1, ys) β tl)
β’ y β hd.2 β¨ β ys, y β ys β§ (hd.1, ys) β tl |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | simp only [Prod.eq_iff_fst_eq_snd_eq] at a1 | case mpr
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
a1 : β ys, y β ys β§ ((hd.1, ys) = hd β¨ (hd.1, ys) β tl)
β’ y β hd.2 β¨ β ys, y β ys β§ (hd.1, ys) β tl | case mpr
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
a1 : β ys, y β ys β§ (True β§ ys = hd.2 β¨ (hd.1, ys) β tl)
β’ y β hd.2 β¨ β ys, y β ys β§ (hd.1, ys) β tl |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | simp at a1 | case mpr
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
a1 : β ys, y β ys β§ (True β§ ys = hd.2 β¨ (hd.1, ys) β tl)
β’ y β hd.2 β¨ β ys, y β ys β§ (hd.1, ys) β tl | case mpr
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
a1 : β ys, y β ys β§ (ys = hd.2 β¨ (hd.1, ys) β tl)
β’ y β hd.2 β¨ β ys, y β ys β§ (hd.1, ys) β tl |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | apply Exists.elim a1 | case mpr
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
a1 : β ys, y β ys β§ (ys = hd.2 β¨ (hd.1, ys) β tl)
β’ y β hd.2 β¨ β ys, y β ys β§ (hd.1, ys) β tl | case mpr
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
a1 : β ys, y β ys β§ (ys = hd.2 β¨ (hd.1, ys) β tl)
β’ β (a : List Node), y β a β§ (a = hd.2 β¨ (hd.1, a) β tl) β y β hd.2 β¨ β ys, y β ys β§ (hd.1, ys) β tl |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | intro zs a2 | case mpr
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
a1 : β ys, y β ys β§ (ys = hd.2 β¨ (hd.1, ys) β tl)
β’ β (a : List Node), y β a β§ (a = hd.2 β¨ (hd.1, a) β tl) β y β hd.2 β¨ β ys, y β ys β§ (hd.1, ys) β tl | case mpr
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
a1 : β ys, y β ys β§ (ys = hd.2 β¨ (hd.1, ys) β tl)
zs : List Node
a2 : y β zs β§ (zs = hd.2 β¨ (hd.1, zs) β tl)
β’ y β hd.2 β¨ β ys, y β ys β§ (hd.1, ys) β tl |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | cases a2 | case mpr
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
a1 : β ys, y β ys β§ (ys = hd.2 β¨ (hd.1, ys) β tl)
zs : List Node
a2 : y β zs β§ (zs = hd.2 β¨ (hd.1, zs) β tl)
β’ y β hd.2 β¨ β ys, y β ys β§ (hd.1, ys) β tl | case mpr.intro
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
a1 : β ys, y β ys β§ (ys = hd.2 β¨ (hd.1, ys) β tl)
zs : List Node
leftβ : y β zs
rightβ : zs = hd.2 β¨ (hd.1, zs) β tl
β’ y β hd.2 β¨ β ys, y β ys β§ (hd.1, ys) β tl |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | case _ a2_left a2_right =>
cases a2_right
case _ left =>
subst left
tauto
case _ right =>
right
apply Exists.intro zs
tauto | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
a1 : β ys, y β ys β§ (ys = hd.2 β¨ (hd.1, ys) β tl)
zs : List Node
a2_left : y β zs
a2_right : zs = hd.2 β¨ (hd.1, zs) β tl
β’ y β hd.2 β¨ β ys, y β ys β§ (hd.1, ys) β tl | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | cases a2_right | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
a1 : β ys, y β ys β§ (ys = hd.2 β¨ (hd.1, ys) β tl)
zs : List Node
a2_left : y β zs
a2_right : zs = hd.2 β¨ (hd.1, zs) β tl
β’ y β hd.2 β¨ β ys, y β ys β§ (hd.1, ys) β tl | case inl
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
a1 : β ys, y β ys β§ (ys = hd.2 β¨ (hd.1, ys) β tl)
zs : List Node
a2_left : y β zs
hβ : zs = hd.2
β’ y β hd.2 β¨ β ys, y β ys β§ (hd.1, ys) β tl
case inr
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
a1 : β ys, y β ys β§ (ys = hd.2 β¨ (hd.1, ys) β tl)
zs : List Node
a2_left : y β zs
hβ : (hd.1, zs) β tl
β’ y β hd.2 β¨ β ys, y β ys β§ (hd.1, ys) β tl |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | case _ left =>
subst left
tauto | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
a1 : β ys, y β ys β§ (ys = hd.2 β¨ (hd.1, ys) β tl)
zs : List Node
a2_left : y β zs
left : zs = hd.2
β’ y β hd.2 β¨ β ys, y β ys β§ (hd.1, ys) β tl | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | case _ right =>
right
apply Exists.intro zs
tauto | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
a1 : β ys, y β ys β§ (ys = hd.2 β¨ (hd.1, ys) β tl)
zs : List Node
a2_left : y β zs
right : (hd.1, zs) β tl
β’ y β hd.2 β¨ β ys, y β ys β§ (hd.1, ys) β tl | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | subst left | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
a1 : β ys, y β ys β§ (ys = hd.2 β¨ (hd.1, ys) β tl)
zs : List Node
a2_left : y β zs
left : zs = hd.2
β’ y β hd.2 β¨ β ys, y β ys β§ (hd.1, ys) β tl | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
a1 : β ys, y β ys β§ (ys = hd.2 β¨ (hd.1, ys) β tl)
a2_left : y β hd.2
β’ y β hd.2 β¨ β ys, y β ys β§ (hd.1, ys) β tl |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | tauto | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
a1 : β ys, y β ys β§ (ys = hd.2 β¨ (hd.1, ys) β tl)
a2_left : y β hd.2
β’ y β hd.2 β¨ β ys, y β ys β§ (hd.1, ys) β tl | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | right | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
a1 : β ys, y β ys β§ (ys = hd.2 β¨ (hd.1, ys) β tl)
zs : List Node
a2_left : y β zs
right : (hd.1, zs) β tl
β’ y β hd.2 β¨ β ys, y β ys β§ (hd.1, ys) β tl | case h
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
a1 : β ys, y β ys β§ (ys = hd.2 β¨ (hd.1, ys) β tl)
zs : List Node
a2_left : y β zs
right : (hd.1, zs) β tl
β’ β ys, y β ys β§ (hd.1, ys) β tl |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | apply Exists.intro zs | case h
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
a1 : β ys, y β ys β§ (ys = hd.2 β¨ (hd.1, ys) β tl)
zs : List Node
a2_left : y β zs
right : (hd.1, zs) β tl
β’ β ys, y β ys β§ (hd.1, ys) β tl | case h
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
a1 : β ys, y β ys β§ (ys = hd.2 β¨ (hd.1, ys) β tl)
zs : List Node
a2_left : y β zs
right : (hd.1, zs) β tl
β’ y β zs β§ (hd.1, zs) β tl |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | tauto | case h
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
y : Node
a1 : β ys, y β ys β§ (ys = hd.2 β¨ (hd.1, ys) β tl)
zs : List Node
a2_left : y β zs
right : (hd.1, zs) β tl
β’ y β zs β§ (hd.1, zs) β tl | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | simp | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
x y : Node
c1 : Β¬hd.1 = x
β’ y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β hd :: tl | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
x y : Node
c1 : Β¬hd.1 = x
β’ y β direct_succ_list tl x β β ys, y β ys β§ ((x, ys) = hd β¨ (x, ys) β tl) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | simp only [ih] | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
x y : Node
c1 : Β¬hd.1 = x
β’ y β direct_succ_list tl x β β ys, y β ys β§ ((x, ys) = hd β¨ (x, ys) β tl) | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
x y : Node
c1 : Β¬hd.1 = x
β’ (β ys, y β ys β§ (x, ys) β tl) β β ys, y β ys β§ ((x, ys) = hd β¨ (x, ys) β tl) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | constructor | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
x y : Node
c1 : Β¬hd.1 = x
β’ (β ys, y β ys β§ (x, ys) β tl) β β ys, y β ys β§ ((x, ys) = hd β¨ (x, ys) β tl) | case mp
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
x y : Node
c1 : Β¬hd.1 = x
β’ (β ys, y β ys β§ (x, ys) β tl) β β ys, y β ys β§ ((x, ys) = hd β¨ (x, ys) β tl)
case mpr
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
x y : Node
c1 : Β¬hd.1 = x
β’ (β ys, y β ys β§ ((x, ys) = hd β¨ (x, ys) β tl)) β β ys, y β ys β§ (x, ys) β tl |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | intro a1 | case mp
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
x y : Node
c1 : Β¬hd.1 = x
β’ (β ys, y β ys β§ (x, ys) β tl) β β ys, y β ys β§ ((x, ys) = hd β¨ (x, ys) β tl) | case mp
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
x y : Node
c1 : Β¬hd.1 = x
a1 : β ys, y β ys β§ (x, ys) β tl
β’ β ys, y β ys β§ ((x, ys) = hd β¨ (x, ys) β tl) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | apply Exists.elim a1 | case mp
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
x y : Node
c1 : Β¬hd.1 = x
a1 : β ys, y β ys β§ (x, ys) β tl
β’ β ys, y β ys β§ ((x, ys) = hd β¨ (x, ys) β tl) | case mp
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
x y : Node
c1 : Β¬hd.1 = x
a1 : β ys, y β ys β§ (x, ys) β tl
β’ β (a : List Node), y β a β§ (x, a) β tl β β ys, y β ys β§ ((x, ys) = hd β¨ (x, ys) β tl) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | intro zs a2 | case mp
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
x y : Node
c1 : Β¬hd.1 = x
a1 : β ys, y β ys β§ (x, ys) β tl
β’ β (a : List Node), y β a β§ (x, a) β tl β β ys, y β ys β§ ((x, ys) = hd β¨ (x, ys) β tl) | case mp
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
x y : Node
c1 : Β¬hd.1 = x
a1 : β ys, y β ys β§ (x, ys) β tl
zs : List Node
a2 : y β zs β§ (x, zs) β tl
β’ β ys, y β ys β§ ((x, ys) = hd β¨ (x, ys) β tl) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | cases a2 | case mp
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
x y : Node
c1 : Β¬hd.1 = x
a1 : β ys, y β ys β§ (x, ys) β tl
zs : List Node
a2 : y β zs β§ (x, zs) β tl
β’ β ys, y β ys β§ ((x, ys) = hd β¨ (x, ys) β tl) | case mp.intro
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
x y : Node
c1 : Β¬hd.1 = x
a1 : β ys, y β ys β§ (x, ys) β tl
zs : List Node
leftβ : y β zs
rightβ : (x, zs) β tl
β’ β ys, y β ys β§ ((x, ys) = hd β¨ (x, ys) β tl) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | case _ a2_left a2_right =>
apply Exists.intro zs
tauto | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
x y : Node
c1 : Β¬hd.1 = x
a1 : β ys, y β ys β§ (x, ys) β tl
zs : List Node
a2_left : y β zs
a2_right : (x, zs) β tl
β’ β ys, y β ys β§ ((x, ys) = hd β¨ (x, ys) β tl) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | apply Exists.intro zs | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
x y : Node
c1 : Β¬hd.1 = x
a1 : β ys, y β ys β§ (x, ys) β tl
zs : List Node
a2_left : y β zs
a2_right : (x, zs) β tl
β’ β ys, y β ys β§ ((x, ys) = hd β¨ (x, ys) β tl) | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
x y : Node
c1 : Β¬hd.1 = x
a1 : β ys, y β ys β§ (x, ys) β tl
zs : List Node
a2_left : y β zs
a2_right : (x, zs) β tl
β’ y β zs β§ ((x, zs) = hd β¨ (x, zs) β tl) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | tauto | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
x y : Node
c1 : Β¬hd.1 = x
a1 : β ys, y β ys β§ (x, ys) β tl
zs : List Node
a2_left : y β zs
a2_right : (x, zs) β tl
β’ y β zs β§ ((x, zs) = hd β¨ (x, zs) β tl) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | intro a1 | case mpr
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
x y : Node
c1 : Β¬hd.1 = x
β’ (β ys, y β ys β§ ((x, ys) = hd β¨ (x, ys) β tl)) β β ys, y β ys β§ (x, ys) β tl | case mpr
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
x y : Node
c1 : Β¬hd.1 = x
a1 : β ys, y β ys β§ ((x, ys) = hd β¨ (x, ys) β tl)
β’ β ys, y β ys β§ (x, ys) β tl |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | simp only [Prod.eq_iff_fst_eq_snd_eq] at a1 | case mpr
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
x y : Node
c1 : Β¬hd.1 = x
a1 : β ys, y β ys β§ ((x, ys) = hd β¨ (x, ys) β tl)
β’ β ys, y β ys β§ (x, ys) β tl | case mpr
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
x y : Node
c1 : Β¬hd.1 = x
a1 : β ys, y β ys β§ (x = hd.1 β§ ys = hd.2 β¨ (x, ys) β tl)
β’ β ys, y β ys β§ (x, ys) β tl |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_direct_succ_list_iff | [65, 1] | [122, 16] | tauto | case mpr
Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : β (x y : Node), y β direct_succ_list tl x β β ys, y β ys β§ (x, ys) β tl
x y : Node
c1 : Β¬hd.1 = x
a1 : β ys, y β ys β§ (x = hd.1 β§ ys = hd.2 β¨ (x, ys) β tl)
β’ β ys, y β ys β§ (x, ys) β tl | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | direct_succ_list_set_equiv | [125, 1] | [135, 41] | ext a | Node : Type
instβ : DecidableEq Node
g : Graph Node
x : Node
β’ β(direct_succ_list g x).toFinset = direct_succ_set g x | case h
Node : Type
instβ : DecidableEq Node
g : Graph Node
x a : Node
β’ a β β(direct_succ_list g x).toFinset β a β direct_succ_set g x |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | direct_succ_list_set_equiv | [125, 1] | [135, 41] | simp only [direct_succ_set] | case h
Node : Type
instβ : DecidableEq Node
g : Graph Node
x a : Node
β’ a β β(direct_succ_list g x).toFinset β a β direct_succ_set g x | case h
Node : Type
instβ : DecidableEq Node
g : Graph Node
x a : Node
β’ a β β(direct_succ_list g x).toFinset β a β {y | β ys, y β ys β§ (x, ys) β g} |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | direct_succ_list_set_equiv | [125, 1] | [135, 41] | simp | case h
Node : Type
instβ : DecidableEq Node
g : Graph Node
x a : Node
β’ a β β(direct_succ_list g x).toFinset β a β {y | β ys, y β ys β§ (x, ys) β g} | case h
Node : Type
instβ : DecidableEq Node
g : Graph Node
x a : Node
β’ a β direct_succ_list g x β β ys, a β ys β§ (x, ys) β g |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | direct_succ_list_set_equiv | [125, 1] | [135, 41] | simp only [mem_direct_succ_list_iff] | case h
Node : Type
instβ : DecidableEq Node
g : Graph Node
x a : Node
β’ a β direct_succ_list g x β β ys, a β ys β§ (x, ys) β g | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_list_direct_succ_list_iff | [164, 1] | [172, 9] | simp only [list_direct_succ_list] | Node : Type
instβ : DecidableEq Node
g : Graph Node
β’ β (xs : List Node) (y : Node), y β list_direct_succ_list g xs β β x β xs, β ys, y β ys β§ (x, ys) β g | Node : Type
instβ : DecidableEq Node
g : Graph Node
β’ β (xs : List Node) (y : Node),
y β (List.map (fun x => direct_succ_list g x) xs).join β β x β xs, β ys, y β ys β§ (x, ys) β g |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_list_direct_succ_list_iff | [164, 1] | [172, 9] | simp only [β mem_direct_succ_list_iff] | Node : Type
instβ : DecidableEq Node
g : Graph Node
β’ β (xs : List Node) (y : Node),
y β (List.map (fun x => direct_succ_list g x) xs).join β β x β xs, β ys, y β ys β§ (x, ys) β g | Node : Type
instβ : DecidableEq Node
g : Graph Node
β’ β (xs : List Node) (y : Node),
y β (List.map (fun x => direct_succ_list g x) xs).join β β x β xs, y β direct_succ_list g x |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | mem_list_direct_succ_list_iff | [164, 1] | [172, 9] | simp | Node : Type
instβ : DecidableEq Node
g : Graph Node
β’ β (xs : List Node) (y : Node),
y β (List.map (fun x => direct_succ_list g x) xs).join β β x β xs, y β direct_succ_list g x | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | list_direct_succ_list_set_equiv | [175, 1] | [184, 9] | simp only [list_direct_succ_set] | Node : Type
instβ : DecidableEq Node
g : Graph Node
xs : List Node
β’ β(list_direct_succ_list g xs).toFinset = list_direct_succ_set g xs | Node : Type
instβ : DecidableEq Node
g : Graph Node
xs : List Node
β’ β(list_direct_succ_list g xs).toFinset = {y | β x β xs, β ys, y β ys β§ (x, ys) β g} |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | list_direct_succ_list_set_equiv | [175, 1] | [184, 9] | simp only [β mem_list_direct_succ_list_iff] | Node : Type
instβ : DecidableEq Node
g : Graph Node
xs : List Node
β’ β(list_direct_succ_list g xs).toFinset = {y | β x β xs, β ys, y β ys β§ (x, ys) β g} | Node : Type
instβ : DecidableEq Node
g : Graph Node
xs : List Node
β’ β(list_direct_succ_list g xs).toFinset = {y | y β list_direct_succ_list g xs} |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | list_direct_succ_list_set_equiv | [175, 1] | [184, 9] | simp | Node : Type
instβ : DecidableEq Node
g : Graph Node
xs : List Node
β’ β(list_direct_succ_list g xs).toFinset = {y | y β list_direct_succ_list g xs} | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | list_direct_succ_list_cons | [187, 1] | [196, 9] | simp only [list_direct_succ_list] | Node : Type
instβ : DecidableEq Node
g : Graph Node
x : Node
xs : List Node
β’ list_direct_succ_list g (x :: xs) = direct_succ_list g x ++ list_direct_succ_list g xs | Node : Type
instβ : DecidableEq Node
g : Graph Node
x : Node
xs : List Node
β’ (List.map (fun x => direct_succ_list g x) (x :: xs)).join =
direct_succ_list g x ++ (List.map (fun x => direct_succ_list g x) xs).join |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | list_direct_succ_list_cons | [187, 1] | [196, 9] | simp | Node : Type
instβ : DecidableEq Node
g : Graph Node
x : Node
xs : List Node
β’ (List.map (fun x => direct_succ_list g x) (x :: xs)).join =
direct_succ_list g x ++ (List.map (fun x => direct_succ_list g x) xs).join | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | list_direct_succ_set_cons | [199, 1] | [210, 8] | simp only [list_direct_succ_set] | Node : Type
instβ : DecidableEq Node
g : Graph Node
x : Node
xs : List Node
β’ list_direct_succ_set g (x :: xs) = β(direct_succ_list g x).toFinset βͺ list_direct_succ_set g xs | Node : Type
instβ : DecidableEq Node
g : Graph Node
x : Node
xs : List Node
β’ {y | β x_1 β x :: xs, β ys, y β ys β§ (x_1, ys) β g} =
β(direct_succ_list g x).toFinset βͺ {y | β x β xs, β ys, y β ys β§ (x, ys) β g} |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | list_direct_succ_set_cons | [199, 1] | [210, 8] | simp only [β mem_direct_succ_list_iff] | Node : Type
instβ : DecidableEq Node
g : Graph Node
x : Node
xs : List Node
β’ {y | β x_1 β x :: xs, β ys, y β ys β§ (x_1, ys) β g} =
β(direct_succ_list g x).toFinset βͺ {y | β x β xs, β ys, y β ys β§ (x, ys) β g} | Node : Type
instβ : DecidableEq Node
g : Graph Node
x : Node
xs : List Node
β’ {y | β x_1 β x :: xs, y β direct_succ_list g x_1} =
β(direct_succ_list g x).toFinset βͺ {y | β x β xs, y β direct_succ_list g x} |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | list_direct_succ_set_cons | [199, 1] | [210, 8] | simp | Node : Type
instβ : DecidableEq Node
g : Graph Node
x : Node
xs : List Node
β’ {y | β x_1 β x :: xs, y β direct_succ_list g x_1} =
β(direct_succ_list g x).toFinset βͺ {y | β x β xs, y β direct_succ_list g x} | Node : Type
instβ : DecidableEq Node
g : Graph Node
x : Node
xs : List Node
β’ {y | y β direct_succ_list g x β¨ β a β xs, y β direct_succ_list g a} =
{a | a β direct_succ_list g x} βͺ {y | β x β xs, y β direct_succ_list g x} |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | list_direct_succ_set_cons | [199, 1] | [210, 8] | rfl | Node : Type
instβ : DecidableEq Node
g : Graph Node
x : Node
xs : List Node
β’ {y | y β direct_succ_list g x β¨ β a β xs, y β direct_succ_list g a} =
{a | a β direct_succ_list g x} βͺ {y | β x β xs, y β direct_succ_list g x} | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | not_mem_imp_no_direct_succ | [227, 1] | [251, 14] | induction g | Node : Type
instβ : DecidableEq Node
g : Graph Node
x : Node
h1 : x β g.nodes_of
β’ direct_succ_list g x = [] | case nil
Node : Type
instβ : DecidableEq Node
x : Node
h1 : x β Graph.nodes_of []
β’ direct_succ_list [] x = []
case cons
Node : Type
instβ : DecidableEq Node
x : Node
headβ : Node Γ List Node
tailβ : List (Node Γ List Node)
tail_ihβ : x β Graph.nodes_of tailβ β direct_succ_list tailβ x = []
h1 : x β Graph.nodes_of (headβ :: tailβ)
β’ direct_succ_list (headβ :: tailβ) x = [] |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | not_mem_imp_no_direct_succ | [227, 1] | [251, 14] | case nil =>
simp only [direct_succ_list] | Node : Type
instβ : DecidableEq Node
x : Node
h1 : x β Graph.nodes_of []
β’ direct_succ_list [] x = [] | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | not_mem_imp_no_direct_succ | [227, 1] | [251, 14] | case cons hd tl ih =>
simp only [Graph.nodes_of] at ih
simp at ih
simp only [Graph.nodes_of] at h1
simp at h1
simp only [direct_succ_list]
split_ifs
case pos c1 =>
subst c1
simp at h1
case neg c1 =>
tauto | Node : Type
instβ : DecidableEq Node
x : Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : x β Graph.nodes_of tl β direct_succ_list tl x = []
h1 : x β Graph.nodes_of (hd :: tl)
β’ direct_succ_list (hd :: tl) x = [] | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | not_mem_imp_no_direct_succ | [227, 1] | [251, 14] | simp only [direct_succ_list] | Node : Type
instβ : DecidableEq Node
x : Node
h1 : x β Graph.nodes_of []
β’ direct_succ_list [] x = [] | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | not_mem_imp_no_direct_succ | [227, 1] | [251, 14] | simp only [Graph.nodes_of] at ih | Node : Type
instβ : DecidableEq Node
x : Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : x β Graph.nodes_of tl β direct_succ_list tl x = []
h1 : x β Graph.nodes_of (hd :: tl)
β’ direct_succ_list (hd :: tl) x = [] | Node : Type
instβ : DecidableEq Node
x : Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : x β List.map Prod.fst tl βͺ (List.map Prod.snd tl).join β direct_succ_list tl x = []
h1 : x β Graph.nodes_of (hd :: tl)
β’ direct_succ_list (hd :: tl) x = [] |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | not_mem_imp_no_direct_succ | [227, 1] | [251, 14] | simp at ih | Node : Type
instβ : DecidableEq Node
x : Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih : x β List.map Prod.fst tl βͺ (List.map Prod.snd tl).join β direct_succ_list tl x = []
h1 : x β Graph.nodes_of (hd :: tl)
β’ direct_succ_list (hd :: tl) x = [] | Node : Type
instβ : DecidableEq Node
x : Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
h1 : x β Graph.nodes_of (hd :: tl)
ih :
(β (x_1 : List Node), (x, x_1) β tl) β
(β (x_1 : List Node) (x_2 : Node), (x_2, x_1) β tl β x β x_1) β direct_succ_list tl x = []
β’ direct_succ_list (hd :: tl) x = [] |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | not_mem_imp_no_direct_succ | [227, 1] | [251, 14] | simp only [Graph.nodes_of] at h1 | Node : Type
instβ : DecidableEq Node
x : Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
h1 : x β Graph.nodes_of (hd :: tl)
ih :
(β (x_1 : List Node), (x, x_1) β tl) β
(β (x_1 : List Node) (x_2 : Node), (x_2, x_1) β tl β x β x_1) β direct_succ_list tl x = []
β’ direct_succ_list (hd :: tl) x = [] | Node : Type
instβ : DecidableEq Node
x : Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
h1 : x β List.map Prod.fst (hd :: tl) βͺ (List.map Prod.snd (hd :: tl)).join
ih :
(β (x_1 : List Node), (x, x_1) β tl) β
(β (x_1 : List Node) (x_2 : Node), (x_2, x_1) β tl β x β x_1) β direct_succ_list tl x = []
β’ direct_succ_list (hd :: tl) x = [] |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | not_mem_imp_no_direct_succ | [227, 1] | [251, 14] | simp at h1 | Node : Type
instβ : DecidableEq Node
x : Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
h1 : x β List.map Prod.fst (hd :: tl) βͺ (List.map Prod.snd (hd :: tl)).join
ih :
(β (x_1 : List Node), (x, x_1) β tl) β
(β (x_1 : List Node) (x_2 : Node), (x_2, x_1) β tl β x β x_1) β direct_succ_list tl x = []
β’ direct_succ_list (hd :: tl) x = [] | Node : Type
instβ : DecidableEq Node
x : Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih :
(β (x_1 : List Node), (x, x_1) β tl) β
(β (x_1 : List Node) (x_2 : Node), (x_2, x_1) β tl β x β x_1) β direct_succ_list tl x = []
h1 :
Β¬x = hd.1 β§
(β (x_1 : List Node), (x, x_1) β tl) β§ x β hd.2 β§ β (x_1 : List Node) (x_2 : Node), (x_2, x_1) β tl β x β x_1
β’ direct_succ_list (hd :: tl) x = [] |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | not_mem_imp_no_direct_succ | [227, 1] | [251, 14] | simp only [direct_succ_list] | Node : Type
instβ : DecidableEq Node
x : Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih :
(β (x_1 : List Node), (x, x_1) β tl) β
(β (x_1 : List Node) (x_2 : Node), (x_2, x_1) β tl β x β x_1) β direct_succ_list tl x = []
h1 :
Β¬x = hd.1 β§
(β (x_1 : List Node), (x, x_1) β tl) β§ x β hd.2 β§ β (x_1 : List Node) (x_2 : Node), (x_2, x_1) β tl β x β x_1
β’ direct_succ_list (hd :: tl) x = [] | Node : Type
instβ : DecidableEq Node
x : Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih :
(β (x_1 : List Node), (x, x_1) β tl) β
(β (x_1 : List Node) (x_2 : Node), (x_2, x_1) β tl β x β x_1) β direct_succ_list tl x = []
h1 :
Β¬x = hd.1 β§
(β (x_1 : List Node), (x, x_1) β tl) β§ x β hd.2 β§ β (x_1 : List Node) (x_2 : Node), (x_2, x_1) β tl β x β x_1
β’ (if hd.1 = x then hd.2 ++ direct_succ_list tl x else direct_succ_list tl x) = [] |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | not_mem_imp_no_direct_succ | [227, 1] | [251, 14] | split_ifs | Node : Type
instβ : DecidableEq Node
x : Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih :
(β (x_1 : List Node), (x, x_1) β tl) β
(β (x_1 : List Node) (x_2 : Node), (x_2, x_1) β tl β x β x_1) β direct_succ_list tl x = []
h1 :
Β¬x = hd.1 β§
(β (x_1 : List Node), (x, x_1) β tl) β§ x β hd.2 β§ β (x_1 : List Node) (x_2 : Node), (x_2, x_1) β tl β x β x_1
β’ (if hd.1 = x then hd.2 ++ direct_succ_list tl x else direct_succ_list tl x) = [] | case pos
Node : Type
instβ : DecidableEq Node
x : Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih :
(β (x_1 : List Node), (x, x_1) β tl) β
(β (x_1 : List Node) (x_2 : Node), (x_2, x_1) β tl β x β x_1) β direct_succ_list tl x = []
h1 :
Β¬x = hd.1 β§
(β (x_1 : List Node), (x, x_1) β tl) β§ x β hd.2 β§ β (x_1 : List Node) (x_2 : Node), (x_2, x_1) β tl β x β x_1
hβ : hd.1 = x
β’ hd.2 ++ direct_succ_list tl x = []
case neg
Node : Type
instβ : DecidableEq Node
x : Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih :
(β (x_1 : List Node), (x, x_1) β tl) β
(β (x_1 : List Node) (x_2 : Node), (x_2, x_1) β tl β x β x_1) β direct_succ_list tl x = []
h1 :
Β¬x = hd.1 β§
(β (x_1 : List Node), (x, x_1) β tl) β§ x β hd.2 β§ β (x_1 : List Node) (x_2 : Node), (x_2, x_1) β tl β x β x_1
hβ : Β¬hd.1 = x
β’ direct_succ_list tl x = [] |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | not_mem_imp_no_direct_succ | [227, 1] | [251, 14] | case pos c1 =>
subst c1
simp at h1 | Node : Type
instβ : DecidableEq Node
x : Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih :
(β (x_1 : List Node), (x, x_1) β tl) β
(β (x_1 : List Node) (x_2 : Node), (x_2, x_1) β tl β x β x_1) β direct_succ_list tl x = []
h1 :
Β¬x = hd.1 β§
(β (x_1 : List Node), (x, x_1) β tl) β§ x β hd.2 β§ β (x_1 : List Node) (x_2 : Node), (x_2, x_1) β tl β x β x_1
c1 : hd.1 = x
β’ hd.2 ++ direct_succ_list tl x = [] | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | not_mem_imp_no_direct_succ | [227, 1] | [251, 14] | case neg c1 =>
tauto | Node : Type
instβ : DecidableEq Node
x : Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih :
(β (x_1 : List Node), (x, x_1) β tl) β
(β (x_1 : List Node) (x_2 : Node), (x_2, x_1) β tl β x β x_1) β direct_succ_list tl x = []
h1 :
Β¬x = hd.1 β§
(β (x_1 : List Node), (x, x_1) β tl) β§ x β hd.2 β§ β (x_1 : List Node) (x_2 : Node), (x_2, x_1) β tl β x β x_1
c1 : Β¬hd.1 = x
β’ direct_succ_list tl x = [] | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | not_mem_imp_no_direct_succ | [227, 1] | [251, 14] | subst c1 | Node : Type
instβ : DecidableEq Node
x : Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih :
(β (x_1 : List Node), (x, x_1) β tl) β
(β (x_1 : List Node) (x_2 : Node), (x_2, x_1) β tl β x β x_1) β direct_succ_list tl x = []
h1 :
Β¬x = hd.1 β§
(β (x_1 : List Node), (x, x_1) β tl) β§ x β hd.2 β§ β (x_1 : List Node) (x_2 : Node), (x_2, x_1) β tl β x β x_1
c1 : hd.1 = x
β’ hd.2 ++ direct_succ_list tl x = [] | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih :
(β (x : List Node), (hd.1, x) β tl) β
(β (x : List Node) (x_1 : Node), (x_1, x) β tl β hd.1 β x) β direct_succ_list tl hd.1 = []
h1 :
Β¬hd.1 = hd.1 β§
(β (x : List Node), (hd.1, x) β tl) β§ hd.1 β hd.2 β§ β (x : List Node) (x_1 : Node), (x_1, x) β tl β hd.1 β x
β’ hd.2 ++ direct_succ_list tl hd.1 = [] |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | not_mem_imp_no_direct_succ | [227, 1] | [251, 14] | simp at h1 | Node : Type
instβ : DecidableEq Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih :
(β (x : List Node), (hd.1, x) β tl) β
(β (x : List Node) (x_1 : Node), (x_1, x) β tl β hd.1 β x) β direct_succ_list tl hd.1 = []
h1 :
Β¬hd.1 = hd.1 β§
(β (x : List Node), (hd.1, x) β tl) β§ hd.1 β hd.2 β§ β (x : List Node) (x_1 : Node), (x_1, x) β tl β hd.1 β x
β’ hd.2 ++ direct_succ_list tl hd.1 = [] | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | not_mem_imp_no_direct_succ | [227, 1] | [251, 14] | tauto | Node : Type
instβ : DecidableEq Node
x : Node
hd : Node Γ List Node
tl : List (Node Γ List Node)
ih :
(β (x_1 : List Node), (x, x_1) β tl) β
(β (x_1 : List Node) (x_2 : Node), (x_2, x_1) β tl β x β x_1) β direct_succ_list tl x = []
h1 :
Β¬x = hd.1 β§
(β (x_1 : List Node), (x, x_1) β tl) β§ x β hd.2 β§ β (x_1 : List Node) (x_2 : Node), (x_2, x_1) β tl β x β x_1
c1 : Β¬hd.1 = x
β’ direct_succ_list tl x = [] | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | List.erase_diff_len_lt_diff_len | [254, 1] | [272, 26] | simp only [β List.diff_erase] | Ξ± : Type
instβ : DecidableEq Ξ±
l1 l2 : List Ξ±
x : Ξ±
h1 : x β l1
h2 : x β l2
β’ ((l1.erase x).diff l2).length < (l1.diff l2).length | Ξ± : Type
instβ : DecidableEq Ξ±
l1 l2 : List Ξ±
x : Ξ±
h1 : x β l1
h2 : x β l2
β’ ((l1.diff l2).erase x).length < (l1.diff l2).length |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | List.erase_diff_len_lt_diff_len | [254, 1] | [272, 26] | have s1 : x β l1.diff l2 := List.mem_diff_of_mem h1 h2 | Ξ± : Type
instβ : DecidableEq Ξ±
l1 l2 : List Ξ±
x : Ξ±
h1 : x β l1
h2 : x β l2
β’ ((l1.diff l2).erase x).length < (l1.diff l2).length | Ξ± : Type
instβ : DecidableEq Ξ±
l1 l2 : List Ξ±
x : Ξ±
h1 : x β l1
h2 : x β l2
s1 : x β l1.diff l2
β’ ((l1.diff l2).erase x).length < (l1.diff l2).length |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | List.erase_diff_len_lt_diff_len | [254, 1] | [272, 26] | have s2 : ((l1.diff l2).erase x).length = (l1.diff l2).length.pred := List.length_erase_of_mem s1 | Ξ± : Type
instβ : DecidableEq Ξ±
l1 l2 : List Ξ±
x : Ξ±
h1 : x β l1
h2 : x β l2
s1 : x β l1.diff l2
β’ ((l1.diff l2).erase x).length < (l1.diff l2).length | Ξ± : Type
instβ : DecidableEq Ξ±
l1 l2 : List Ξ±
x : Ξ±
h1 : x β l1
h2 : x β l2
s1 : x β l1.diff l2
s2 : ((l1.diff l2).erase x).length = (l1.diff l2).length.pred
β’ ((l1.diff l2).erase x).length < (l1.diff l2).length |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | List.erase_diff_len_lt_diff_len | [254, 1] | [272, 26] | simp only [s2] | Ξ± : Type
instβ : DecidableEq Ξ±
l1 l2 : List Ξ±
x : Ξ±
h1 : x β l1
h2 : x β l2
s1 : x β l1.diff l2
s2 : ((l1.diff l2).erase x).length = (l1.diff l2).length.pred
β’ ((l1.diff l2).erase x).length < (l1.diff l2).length | Ξ± : Type
instβ : DecidableEq Ξ±
l1 l2 : List Ξ±
x : Ξ±
h1 : x β l1
h2 : x β l2
s1 : x β l1.diff l2
s2 : ((l1.diff l2).erase x).length = (l1.diff l2).length.pred
β’ (l1.diff l2).length.pred < (l1.diff l2).length |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | List.erase_diff_len_lt_diff_len | [254, 1] | [272, 26] | have s3 : 0 < (l1.diff l2).length := List.length_pos_of_mem s1 | Ξ± : Type
instβ : DecidableEq Ξ±
l1 l2 : List Ξ±
x : Ξ±
h1 : x β l1
h2 : x β l2
s1 : x β l1.diff l2
s2 : ((l1.diff l2).erase x).length = (l1.diff l2).length.pred
β’ (l1.diff l2).length.pred < (l1.diff l2).length | Ξ± : Type
instβ : DecidableEq Ξ±
l1 l2 : List Ξ±
x : Ξ±
h1 : x β l1
h2 : x β l2
s1 : x β l1.diff l2
s2 : ((l1.diff l2).erase x).length = (l1.diff l2).length.pred
s3 : 0 < (l1.diff l2).length
β’ (l1.diff l2).length.pred < (l1.diff l2).length |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | List.erase_diff_len_lt_diff_len | [254, 1] | [272, 26] | exact Nat.pred_lt' s3 | Ξ± : Type
instβ : DecidableEq Ξ±
l1 l2 : List Ξ±
x : Ξ±
h1 : x β l1
h2 : x β l2
s1 : x β l1.diff l2
s2 : ((l1.diff l2).erase x).length = (l1.diff l2).length.pred
s3 : 0 < (l1.diff l2).length
β’ (l1.diff l2).length.pred < (l1.diff l2).length | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | dft_aux_cons | [346, 1] | [357, 26] | simp only [dft_aux] | Node : Type
instβ : DecidableEq Node
g : Graph Node
stack visited : List Node
x : Node
h1 : x β visited
β’ dft_aux g (x :: stack) visited = dft_aux g stack visited | Node : Type
instβ : DecidableEq Node
g : Graph Node
stack visited : List Node
x : Node
h1 : x β visited
β’ (if x β visited then dft_aux g stack visited else dft_aux g (direct_succ_list g x ++ stack) (x :: visited)) =
dft_aux g stack visited |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | dft_aux_cons | [346, 1] | [357, 26] | simp only [if_pos h1] | Node : Type
instβ : DecidableEq Node
g : Graph Node
stack visited : List Node
x : Node
h1 : x β visited
β’ (if x β visited then dft_aux g stack visited else dft_aux g (direct_succ_list g x ++ stack) (x :: visited)) =
dft_aux g stack visited | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | dft_aux_append | [360, 1] | [385, 28] | induction xs, zs using dft_aux.induct g | Node : Type
instβ : DecidableEq Node
g : Graph Node
xs ys zs : List Node
β’ dft_aux g (xs ++ ys) zs = dft_aux g ys (dft_aux g xs zs) | case case1
Node : Type
instβ : DecidableEq Node
g : Graph Node
ys visitedβ : List Node
β’ dft_aux g ([] ++ ys) visitedβ = dft_aux g ys (dft_aux g [] visitedβ)
case case2
Node : Type
instβ : DecidableEq Node
g : Graph Node
ys visitedβ : List Node
xβ : Node
xsβ : List Node
hβ : xβ β visitedβ
ih1β : dft_aux g (xsβ ++ ys) visitedβ = dft_aux g ys (dft_aux g xsβ visitedβ)
β’ dft_aux g (xβ :: xsβ ++ ys) visitedβ = dft_aux g ys (dft_aux g (xβ :: xsβ) visitedβ)
case case3
Node : Type
instβ : DecidableEq Node
g : Graph Node
ys visitedβ : List Node
xβ : Node
xsβ : List Node
hβ : xβ β visitedβ
ih1β :
dft_aux g (direct_succ_list g xβ ++ xsβ ++ ys) (xβ :: visitedβ) =
dft_aux g ys (dft_aux g (direct_succ_list g xβ ++ xsβ) (xβ :: visitedβ))
β’ dft_aux g (xβ :: xsβ ++ ys) visitedβ = dft_aux g ys (dft_aux g (xβ :: xsβ) visitedβ) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | dft_aux_append | [360, 1] | [385, 28] | case _ visited =>
simp only [dft_aux]
simp | Node : Type
instβ : DecidableEq Node
g : Graph Node
ys visited : List Node
β’ dft_aux g ([] ++ ys) visited = dft_aux g ys (dft_aux g [] visited) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | dft_aux_append | [360, 1] | [385, 28] | case _ visited x xs c1 ih =>
simp only [dft_aux]
simp only [if_pos c1]
simp only [β ih]
simp
simp only [dft_aux]
simp only [if_pos c1] | Node : Type
instβ : DecidableEq Node
g : Graph Node
ys visited : List Node
x : Node
xs : List Node
c1 : x β visited
ih : dft_aux g (xs ++ ys) visited = dft_aux g ys (dft_aux g xs visited)
β’ dft_aux g (x :: xs ++ ys) visited = dft_aux g ys (dft_aux g (x :: xs) visited) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | dft_aux_append | [360, 1] | [385, 28] | case _ visited x xs c1 ih =>
simp only [dft_aux]
simp only [if_neg c1]
simp only [β ih]
simp
simp only [dft_aux]
simp only [if_neg c1] | Node : Type
instβ : DecidableEq Node
g : Graph Node
ys visited : List Node
x : Node
xs : List Node
c1 : x β visited
ih :
dft_aux g (direct_succ_list g x ++ xs ++ ys) (x :: visited) =
dft_aux g ys (dft_aux g (direct_succ_list g x ++ xs) (x :: visited))
β’ dft_aux g (x :: xs ++ ys) visited = dft_aux g ys (dft_aux g (x :: xs) visited) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | dft_aux_append | [360, 1] | [385, 28] | simp only [dft_aux] | Node : Type
instβ : DecidableEq Node
g : Graph Node
ys visited : List Node
β’ dft_aux g ([] ++ ys) visited = dft_aux g ys (dft_aux g [] visited) | Node : Type
instβ : DecidableEq Node
g : Graph Node
ys visited : List Node
β’ dft_aux g ([] ++ ys) visited = dft_aux g ys visited |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | dft_aux_append | [360, 1] | [385, 28] | simp | Node : Type
instβ : DecidableEq Node
g : Graph Node
ys visited : List Node
β’ dft_aux g ([] ++ ys) visited = dft_aux g ys visited | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | dft_aux_append | [360, 1] | [385, 28] | simp only [dft_aux] | Node : Type
instβ : DecidableEq Node
g : Graph Node
ys visited : List Node
x : Node
xs : List Node
c1 : x β visited
ih : dft_aux g (xs ++ ys) visited = dft_aux g ys (dft_aux g xs visited)
β’ dft_aux g (x :: xs ++ ys) visited = dft_aux g ys (dft_aux g (x :: xs) visited) | Node : Type
instβ : DecidableEq Node
g : Graph Node
ys visited : List Node
x : Node
xs : List Node
c1 : x β visited
ih : dft_aux g (xs ++ ys) visited = dft_aux g ys (dft_aux g xs visited)
β’ dft_aux g (x :: xs ++ ys) visited =
dft_aux g ys (if x β visited then dft_aux g xs visited else dft_aux g (direct_succ_list g x ++ xs) (x :: visited)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | dft_aux_append | [360, 1] | [385, 28] | simp only [if_pos c1] | Node : Type
instβ : DecidableEq Node
g : Graph Node
ys visited : List Node
x : Node
xs : List Node
c1 : x β visited
ih : dft_aux g (xs ++ ys) visited = dft_aux g ys (dft_aux g xs visited)
β’ dft_aux g (x :: xs ++ ys) visited =
dft_aux g ys (if x β visited then dft_aux g xs visited else dft_aux g (direct_succ_list g x ++ xs) (x :: visited)) | Node : Type
instβ : DecidableEq Node
g : Graph Node
ys visited : List Node
x : Node
xs : List Node
c1 : x β visited
ih : dft_aux g (xs ++ ys) visited = dft_aux g ys (dft_aux g xs visited)
β’ dft_aux g (x :: xs ++ ys) visited = dft_aux g ys (dft_aux g xs visited) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | dft_aux_append | [360, 1] | [385, 28] | simp only [β ih] | Node : Type
instβ : DecidableEq Node
g : Graph Node
ys visited : List Node
x : Node
xs : List Node
c1 : x β visited
ih : dft_aux g (xs ++ ys) visited = dft_aux g ys (dft_aux g xs visited)
β’ dft_aux g (x :: xs ++ ys) visited = dft_aux g ys (dft_aux g xs visited) | Node : Type
instβ : DecidableEq Node
g : Graph Node
ys visited : List Node
x : Node
xs : List Node
c1 : x β visited
ih : dft_aux g (xs ++ ys) visited = dft_aux g ys (dft_aux g xs visited)
β’ dft_aux g (x :: xs ++ ys) visited = dft_aux g (xs ++ ys) visited |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | dft_aux_append | [360, 1] | [385, 28] | simp | Node : Type
instβ : DecidableEq Node
g : Graph Node
ys visited : List Node
x : Node
xs : List Node
c1 : x β visited
ih : dft_aux g (xs ++ ys) visited = dft_aux g ys (dft_aux g xs visited)
β’ dft_aux g (x :: xs ++ ys) visited = dft_aux g (xs ++ ys) visited | Node : Type
instβ : DecidableEq Node
g : Graph Node
ys visited : List Node
x : Node
xs : List Node
c1 : x β visited
ih : dft_aux g (xs ++ ys) visited = dft_aux g ys (dft_aux g xs visited)
β’ dft_aux g (x :: (xs ++ ys)) visited = dft_aux g (xs ++ ys) visited |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | dft_aux_append | [360, 1] | [385, 28] | simp only [dft_aux] | Node : Type
instβ : DecidableEq Node
g : Graph Node
ys visited : List Node
x : Node
xs : List Node
c1 : x β visited
ih : dft_aux g (xs ++ ys) visited = dft_aux g ys (dft_aux g xs visited)
β’ dft_aux g (x :: (xs ++ ys)) visited = dft_aux g (xs ++ ys) visited | Node : Type
instβ : DecidableEq Node
g : Graph Node
ys visited : List Node
x : Node
xs : List Node
c1 : x β visited
ih : dft_aux g (xs ++ ys) visited = dft_aux g ys (dft_aux g xs visited)
β’ (if x β visited then dft_aux g (xs ++ ys) visited
else dft_aux g (direct_succ_list g x ++ (xs ++ ys)) (x :: visited)) =
dft_aux g (xs ++ ys) visited |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | dft_aux_append | [360, 1] | [385, 28] | simp only [if_pos c1] | Node : Type
instβ : DecidableEq Node
g : Graph Node
ys visited : List Node
x : Node
xs : List Node
c1 : x β visited
ih : dft_aux g (xs ++ ys) visited = dft_aux g ys (dft_aux g xs visited)
β’ (if x β visited then dft_aux g (xs ++ ys) visited
else dft_aux g (direct_succ_list g x ++ (xs ++ ys)) (x :: visited)) =
dft_aux g (xs ++ ys) visited | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | dft_aux_append | [360, 1] | [385, 28] | simp only [dft_aux] | Node : Type
instβ : DecidableEq Node
g : Graph Node
ys visited : List Node
x : Node
xs : List Node
c1 : x β visited
ih :
dft_aux g (direct_succ_list g x ++ xs ++ ys) (x :: visited) =
dft_aux g ys (dft_aux g (direct_succ_list g x ++ xs) (x :: visited))
β’ dft_aux g (x :: xs ++ ys) visited = dft_aux g ys (dft_aux g (x :: xs) visited) | Node : Type
instβ : DecidableEq Node
g : Graph Node
ys visited : List Node
x : Node
xs : List Node
c1 : x β visited
ih :
dft_aux g (direct_succ_list g x ++ xs ++ ys) (x :: visited) =
dft_aux g ys (dft_aux g (direct_succ_list g x ++ xs) (x :: visited))
β’ dft_aux g (x :: xs ++ ys) visited =
dft_aux g ys (if x β visited then dft_aux g xs visited else dft_aux g (direct_succ_list g x ++ xs) (x :: visited)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | dft_aux_append | [360, 1] | [385, 28] | simp only [if_neg c1] | Node : Type
instβ : DecidableEq Node
g : Graph Node
ys visited : List Node
x : Node
xs : List Node
c1 : x β visited
ih :
dft_aux g (direct_succ_list g x ++ xs ++ ys) (x :: visited) =
dft_aux g ys (dft_aux g (direct_succ_list g x ++ xs) (x :: visited))
β’ dft_aux g (x :: xs ++ ys) visited =
dft_aux g ys (if x β visited then dft_aux g xs visited else dft_aux g (direct_succ_list g x ++ xs) (x :: visited)) | Node : Type
instβ : DecidableEq Node
g : Graph Node
ys visited : List Node
x : Node
xs : List Node
c1 : x β visited
ih :
dft_aux g (direct_succ_list g x ++ xs ++ ys) (x :: visited) =
dft_aux g ys (dft_aux g (direct_succ_list g x ++ xs) (x :: visited))
β’ dft_aux g (x :: xs ++ ys) visited = dft_aux g ys (dft_aux g (direct_succ_list g x ++ xs) (x :: visited)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | dft_aux_append | [360, 1] | [385, 28] | simp only [β ih] | Node : Type
instβ : DecidableEq Node
g : Graph Node
ys visited : List Node
x : Node
xs : List Node
c1 : x β visited
ih :
dft_aux g (direct_succ_list g x ++ xs ++ ys) (x :: visited) =
dft_aux g ys (dft_aux g (direct_succ_list g x ++ xs) (x :: visited))
β’ dft_aux g (x :: xs ++ ys) visited = dft_aux g ys (dft_aux g (direct_succ_list g x ++ xs) (x :: visited)) | Node : Type
instβ : DecidableEq Node
g : Graph Node
ys visited : List Node
x : Node
xs : List Node
c1 : x β visited
ih :
dft_aux g (direct_succ_list g x ++ xs ++ ys) (x :: visited) =
dft_aux g ys (dft_aux g (direct_succ_list g x ++ xs) (x :: visited))
β’ dft_aux g (x :: xs ++ ys) visited = dft_aux g (direct_succ_list g x ++ xs ++ ys) (x :: visited) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | dft_aux_append | [360, 1] | [385, 28] | simp | Node : Type
instβ : DecidableEq Node
g : Graph Node
ys visited : List Node
x : Node
xs : List Node
c1 : x β visited
ih :
dft_aux g (direct_succ_list g x ++ xs ++ ys) (x :: visited) =
dft_aux g ys (dft_aux g (direct_succ_list g x ++ xs) (x :: visited))
β’ dft_aux g (x :: xs ++ ys) visited = dft_aux g (direct_succ_list g x ++ xs ++ ys) (x :: visited) | Node : Type
instβ : DecidableEq Node
g : Graph Node
ys visited : List Node
x : Node
xs : List Node
c1 : x β visited
ih :
dft_aux g (direct_succ_list g x ++ xs ++ ys) (x :: visited) =
dft_aux g ys (dft_aux g (direct_succ_list g x ++ xs) (x :: visited))
β’ dft_aux g (x :: (xs ++ ys)) visited = dft_aux g (direct_succ_list g x ++ (xs ++ ys)) (x :: visited) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | dft_aux_append | [360, 1] | [385, 28] | simp only [dft_aux] | Node : Type
instβ : DecidableEq Node
g : Graph Node
ys visited : List Node
x : Node
xs : List Node
c1 : x β visited
ih :
dft_aux g (direct_succ_list g x ++ xs ++ ys) (x :: visited) =
dft_aux g ys (dft_aux g (direct_succ_list g x ++ xs) (x :: visited))
β’ dft_aux g (x :: (xs ++ ys)) visited = dft_aux g (direct_succ_list g x ++ (xs ++ ys)) (x :: visited) | Node : Type
instβ : DecidableEq Node
g : Graph Node
ys visited : List Node
x : Node
xs : List Node
c1 : x β visited
ih :
dft_aux g (direct_succ_list g x ++ xs ++ ys) (x :: visited) =
dft_aux g ys (dft_aux g (direct_succ_list g x ++ xs) (x :: visited))
β’ (if x β visited then dft_aux g (xs ++ ys) visited
else dft_aux g (direct_succ_list g x ++ (xs ++ ys)) (x :: visited)) =
dft_aux g (direct_succ_list g x ++ (xs ++ ys)) (x :: visited) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | dft_aux_append | [360, 1] | [385, 28] | simp only [if_neg c1] | Node : Type
instβ : DecidableEq Node
g : Graph Node
ys visited : List Node
x : Node
xs : List Node
c1 : x β visited
ih :
dft_aux g (direct_succ_list g x ++ xs ++ ys) (x :: visited) =
dft_aux g ys (dft_aux g (direct_succ_list g x ++ xs) (x :: visited))
β’ (if x β visited then dft_aux g (xs ++ ys) visited
else dft_aux g (direct_succ_list g x ++ (xs ++ ys)) (x :: visited)) =
dft_aux g (direct_succ_list g x ++ (xs ++ ys)) (x :: visited) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | visited_subset_dft_aux | [388, 1] | [409, 17] | induction stack, visited using dft_aux.induct g | Node : Type
instβ : DecidableEq Node
g : Graph Node
stack visited : List Node
β’ visited β dft_aux g stack visited | case case1
Node : Type
instβ : DecidableEq Node
g : Graph Node
visitedβ : List Node
β’ visitedβ β dft_aux g [] visitedβ
case case2
Node : Type
instβ : DecidableEq Node
g : Graph Node
visitedβ : List Node
xβ : Node
xsβ : List Node
hβ : xβ β visitedβ
ih1β : visitedβ β dft_aux g xsβ visitedβ
β’ visitedβ β dft_aux g (xβ :: xsβ) visitedβ
case case3
Node : Type
instβ : DecidableEq Node
g : Graph Node
visitedβ : List Node
xβ : Node
xsβ : List Node
hβ : xβ β visitedβ
ih1β : xβ :: visitedβ β dft_aux g (direct_succ_list g xβ ++ xsβ) (xβ :: visitedβ)
β’ visitedβ β dft_aux g (xβ :: xsβ) visitedβ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | visited_subset_dft_aux | [388, 1] | [409, 17] | case _ visited =>
simp only [dft_aux]
simp | Node : Type
instβ : DecidableEq Node
g : Graph Node
visited : List Node
β’ visited β dft_aux g [] visited | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | visited_subset_dft_aux | [388, 1] | [409, 17] | case _ visited x stack c1 ih =>
simp only [dft_aux]
simp only [if_pos c1]
exact ih | Node : Type
instβ : DecidableEq Node
g : Graph Node
visited : List Node
x : Node
stack : List Node
c1 : x β visited
ih : visited β dft_aux g stack visited
β’ visited β dft_aux g (x :: stack) visited | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | visited_subset_dft_aux | [388, 1] | [409, 17] | simp only [dft_aux] | Node : Type
instβ : DecidableEq Node
g : Graph Node
visited : List Node
β’ visited β dft_aux g [] visited | Node : Type
instβ : DecidableEq Node
g : Graph Node
visited : List Node
β’ visited β visited |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | visited_subset_dft_aux | [388, 1] | [409, 17] | simp | Node : Type
instβ : DecidableEq Node
g : Graph Node
visited : List Node
β’ visited β visited | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | visited_subset_dft_aux | [388, 1] | [409, 17] | simp only [dft_aux] | Node : Type
instβ : DecidableEq Node
g : Graph Node
visited : List Node
x : Node
stack : List Node
c1 : x β visited
ih : visited β dft_aux g stack visited
β’ visited β dft_aux g (x :: stack) visited | Node : Type
instβ : DecidableEq Node
g : Graph Node
visited : List Node
x : Node
stack : List Node
c1 : x β visited
ih : visited β dft_aux g stack visited
β’ visited β if x β visited then dft_aux g stack visited else dft_aux g (direct_succ_list g x ++ stack) (x :: visited) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | visited_subset_dft_aux | [388, 1] | [409, 17] | simp only [if_pos c1] | Node : Type
instβ : DecidableEq Node
g : Graph Node
visited : List Node
x : Node
stack : List Node
c1 : x β visited
ih : visited β dft_aux g stack visited
β’ visited β if x β visited then dft_aux g stack visited else dft_aux g (direct_succ_list g x ++ stack) (x :: visited) | Node : Type
instβ : DecidableEq Node
g : Graph Node
visited : List Node
x : Node
stack : List Node
c1 : x β visited
ih : visited β dft_aux g stack visited
β’ visited β dft_aux g stack visited |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/DFT.lean | visited_subset_dft_aux | [388, 1] | [409, 17] | exact ih | Node : Type
instβ : DecidableEq Node
g : Graph Node
visited : List Node
x : Node
stack : List Node
c1 : x β visited
ih : visited β dft_aux g stack visited
β’ visited β dft_aux g stack visited | no goals |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.