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 | input stringlengths 73 2.09M |
|---|---|---|---|---|---|---|---|---|---|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | apply Exists.intro [] | case right
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w xs : List α
a2_left : xs ∈ RegExp.languageOf α ... | case right
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w xs : List α
a2_left : xs ∈ RegExp.languageOf α ... | Please generate a tactic in lean4 to solve the state.
STATE:
case right
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.lan... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | sorry | case right
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w xs : List α
a2_left : xs ∈ RegExp.languageOf α ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.lan... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp only [RegExp.languageOf] | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
⊢ w ∈ RegExp.languageOf α (r.... | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
⊢ w ∈ {x | ∃ r_1 ∈ RegExp.lan... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
⊢ w ∈ {x | ∃ r_1 ∈ RegExp.lan... | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
⊢ (∃ r_1 ∈ RegExp.languageOf ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | constructor | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
⊢ (∃ r_1 ∈ RegExp.languageOf ... | case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
⊢ (∃ r_1 ∈ RegExp.lan... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | intro a1 | case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
⊢ (∃ r_1 ∈ RegExp.lan... | case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
a1 : ∃ r_1 ∈ RegExp.l... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.langua... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | apply Exists.elim a1 | case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
a1 : ∃ r_1 ∈ RegExp.l... | case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
a1 : ∃ r_1 ∈ RegExp.l... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.langua... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | intro xs a2 | case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
a1 : ∃ r_1 ∈ RegExp.l... | case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
a1 : ∃ r_1 ∈ RegExp.l... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.langua... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | clear a1 | case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
a1 : ∃ r_1 ∈ RegExp.l... | case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
xs : List α
a2 : xs ∈... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.langua... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | sorry | case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
xs : List α
a2 : xs ∈... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.langua... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | sorry | case mpr
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
⊢ (∃ r_1 ∈ RegExp.la... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.langu... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp only [RegExp.derivative] | α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
⊢ w ∈ RegExp.languageOf α (RegExp.derivative a e.closure) ↔ a :: w ∈ RegExp.languageOf α e.closure | α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
⊢ w ∈ RegExp.languageOf α ((RegExp.derivative a e).concat e.closure) ↔ a :: w ∈ RegExp.languageOf α e.closure | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
⊢ w ∈ RegExp.languageOf α (RegExp.derivative a e.closure) ↔ a :: w ∈ RegExp.languageOf α e.closu... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp only [RegExp.languageOf] | α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
⊢ w ∈ RegExp.languageOf α ((RegExp.derivative a e).concat e.closure) ↔ a :: w ∈ RegExp.languageOf α e.closure | α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
⊢ w ∈
{x |
∃ r ∈ RegExp.languageOf α (RegExp.derivative a e),
∃ s ∈ {l | ∃ rs, (∀ r ∈ rs, r ∈ RegExp.languageOf α e) ∧ rs.join = l}, ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
⊢ w ∈ RegExp.languageOf α ((RegExp.derivative a e).concat e.closure) ↔ a :: w ∈ RegExp.languageO... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp | α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
⊢ w ∈
{x |
∃ r ∈ RegExp.languageOf α (RegExp.derivative a e),
∃ s ∈ {l | ∃ rs, (∀ r ∈ rs, r ∈ RegExp.languageOf α e) ∧ rs.join = l}, ... | α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
⊢ (∃ r ∈ RegExp.languageOf α (RegExp.derivative a e), ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ∧ r ++ a.join = w) ↔
∃ rs, (∀ r ∈ rs, r ∈ RegExp.language... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
⊢ w ∈
{x |
∃ r ∈ RegExp.languageOf α (RegExp.derivative a e),
∃ s ∈ {l |... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | constructor | α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
⊢ (∃ r ∈ RegExp.languageOf α (RegExp.derivative a e), ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ∧ r ++ a.join = w) ↔
∃ rs, (∀ r ∈ rs, r ∈ RegExp.language... | case mp
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
⊢ (∃ r ∈ RegExp.languageOf α (RegExp.derivative a e), ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ∧ r ++ a.join = w) →
∃ rs, (∀ r ∈ rs, r ∈ RegExp.... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
⊢ (∃ r ∈ RegExp.languageOf α (RegExp.derivative a e), ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | sorry | case mpr
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
⊢ (∃ rs, (∀ r ∈ rs, r ∈ RegExp.languageOf α e) ∧ rs.join = a :: w) →
∃ r ∈ RegExp.languageOf α (RegExp.derivative a e), ∃ a, (∀ r ∈ a, r ∈ RegEx... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
⊢ (∃ rs, (∀ r ∈ rs, r ∈ RegExp.languageOf α e) ∧ rs.join = a :: w) →
∃ r ∈ RegExp.l... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | intro a1 | case mp
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
⊢ (∃ r ∈ RegExp.languageOf α (RegExp.derivative a e), ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ∧ r ++ a.join = w) →
∃ rs, (∀ r ∈ rs, r ∈ RegExp.... | case mp
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
a1 : ∃ r ∈ RegExp.languageOf α (RegExp.derivative a e), ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ∧ r ++ a.join = w
⊢ ∃ rs, (∀ r ∈ rs, r ∈ RegExp.lan... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
⊢ (∃ r ∈ RegExp.languageOf α (RegExp.derivative a e), ∃ a, (∀ r ∈ a, r ∈ RegExp.language... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | apply Exists.elim a1 | case mp
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
a1 : ∃ r ∈ RegExp.languageOf α (RegExp.derivative a e), ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ∧ r ++ a.join = w
⊢ ∃ rs, (∀ r ∈ rs, r ∈ RegExp.lan... | case mp
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
a1 : ∃ r ∈ RegExp.languageOf α (RegExp.derivative a e), ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ∧ r ++ a.join = w
⊢ ∀ (a_1 : List α),
(a_1 ∈ Re... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
a1 : ∃ r ∈ RegExp.languageOf α (RegExp.derivative a e), ∃ a, (∀ r ∈ a, r ∈ RegExp.langua... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | intro xs a2 | case mp
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
a1 : ∃ r ∈ RegExp.languageOf α (RegExp.derivative a e), ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ∧ r ++ a.join = w
⊢ ∀ (a_1 : List α),
(a_1 ∈ Re... | case mp
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
a1 : ∃ r ∈ RegExp.languageOf α (RegExp.derivative a e), ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ∧ r ++ a.join = w
xs : List α
a2 : xs ∈ RegExp.lang... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
a1 : ∃ r ∈ RegExp.languageOf α (RegExp.derivative a e), ∃ a, (∀ r ∈ a, r ∈ RegExp.langua... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | clear a1 | case mp
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
a1 : ∃ r ∈ RegExp.languageOf α (RegExp.derivative a e), ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ∧ r ++ a.join = w
xs : List α
a2 : xs ∈ RegExp.lang... | case mp
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2 : xs ∈ RegExp.languageOf α (RegExp.derivative a e) ∧ ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ∧ xs ++ a.join = w
⊢ ∃ rs, (∀ r ∈ rs, r ∈ RegExp... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
a1 : ∃ r ∈ RegExp.languageOf α (RegExp.derivative a e), ∃ a, (∀ r ∈ a, r ∈ RegExp.langua... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | cases a2 | case mp
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2 : xs ∈ RegExp.languageOf α (RegExp.derivative a e) ∧ ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ∧ xs ++ a.join = w
⊢ ∃ rs, (∀ r ∈ rs, r ∈ RegExp... | case mp.intro
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
left✝ : xs ∈ RegExp.languageOf α (RegExp.derivative a e)
right✝ : ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ∧ xs ++ a.join = w
⊢ ∃ rs, (∀ r ... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2 : xs ∈ RegExp.languageOf α (RegExp.derivative a e) ∧ ∃ a, (∀ r ∈ a, r ∈ RegExp.lan... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | case _ a2_left a2_right =>
apply Exists.elim a2_right
intro ys a3
clear a2_right
cases a3
case _ a3_left a3_right =>
apply Exists.intro [(a :: w)]
simp
simp only [← ih]
sorry | α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2_left : xs ∈ RegExp.languageOf α (RegExp.derivative a e)
a2_right : ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ∧ xs ++ a.join = w
⊢ ∃ rs, (∀ r ∈ rs, r ∈ ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2_left : xs ∈ RegExp.languageOf α (RegExp.derivative a e)
a2_right : ∃ a, (∀ r ∈ a, r ∈ RegE... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | apply Exists.elim a2_right | α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2_left : xs ∈ RegExp.languageOf α (RegExp.derivative a e)
a2_right : ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ∧ xs ++ a.join = w
⊢ ∃ rs, (∀ r ∈ rs, r ∈ ... | α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2_left : xs ∈ RegExp.languageOf α (RegExp.derivative a e)
a2_right : ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ∧ xs ++ a.join = w
⊢ ∀ (a_1 : List (List α... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2_left : xs ∈ RegExp.languageOf α (RegExp.derivative a e)
a2_right : ∃ a, (∀ r ∈ a, r ∈ RegE... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | intro ys a3 | α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2_left : xs ∈ RegExp.languageOf α (RegExp.derivative a e)
a2_right : ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ∧ xs ++ a.join = w
⊢ ∀ (a_1 : List (List α... | α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2_left : xs ∈ RegExp.languageOf α (RegExp.derivative a e)
a2_right : ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ∧ xs ++ a.join = w
ys : List (List α)
a3 :... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2_left : xs ∈ RegExp.languageOf α (RegExp.derivative a e)
a2_right : ∃ a, (∀ r ∈ a, r ∈ RegE... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | clear a2_right | α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2_left : xs ∈ RegExp.languageOf α (RegExp.derivative a e)
a2_right : ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ∧ xs ++ a.join = w
ys : List (List α)
a3 :... | α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2_left : xs ∈ RegExp.languageOf α (RegExp.derivative a e)
ys : List (List α)
a3 : (∀ r ∈ ys, r ∈ RegExp.languageOf α e) ∧ xs ++ ys.join = w
⊢ ∃ rs, (∀ r ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2_left : xs ∈ RegExp.languageOf α (RegExp.derivative a e)
a2_right : ∃ a, (∀ r ∈ a, r ∈ RegE... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | cases a3 | α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2_left : xs ∈ RegExp.languageOf α (RegExp.derivative a e)
ys : List (List α)
a3 : (∀ r ∈ ys, r ∈ RegExp.languageOf α e) ∧ xs ++ ys.join = w
⊢ ∃ rs, (∀ r ... | case intro
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2_left : xs ∈ RegExp.languageOf α (RegExp.derivative a e)
ys : List (List α)
left✝ : ∀ r ∈ ys, r ∈ RegExp.languageOf α e
right✝ : xs ++ ys.joi... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2_left : xs ∈ RegExp.languageOf α (RegExp.derivative a e)
ys : List (List α)
a3 : (∀ r ∈ ys,... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | case _ a3_left a3_right =>
apply Exists.intro [(a :: w)]
simp
simp only [← ih]
sorry | α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2_left : xs ∈ RegExp.languageOf α (RegExp.derivative a e)
ys : List (List α)
a3_left : ∀ r ∈ ys, r ∈ RegExp.languageOf α e
a3_right : xs ++ ys.join = w
⊢... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2_left : xs ∈ RegExp.languageOf α (RegExp.derivative a e)
ys : List (List α)
a3_left : ∀ r ∈... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | apply Exists.intro [(a :: w)] | α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2_left : xs ∈ RegExp.languageOf α (RegExp.derivative a e)
ys : List (List α)
a3_left : ∀ r ∈ ys, r ∈ RegExp.languageOf α e
a3_right : xs ++ ys.join = w
⊢... | α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2_left : xs ∈ RegExp.languageOf α (RegExp.derivative a e)
ys : List (List α)
a3_left : ∀ r ∈ ys, r ∈ RegExp.languageOf α e
a3_right : xs ++ ys.join = w
⊢... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2_left : xs ∈ RegExp.languageOf α (RegExp.derivative a e)
ys : List (List α)
a3_left : ∀ r ∈... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp | α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2_left : xs ∈ RegExp.languageOf α (RegExp.derivative a e)
ys : List (List α)
a3_left : ∀ r ∈ ys, r ∈ RegExp.languageOf α e
a3_right : xs ++ ys.join = w
⊢... | α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2_left : xs ∈ RegExp.languageOf α (RegExp.derivative a e)
ys : List (List α)
a3_left : ∀ r ∈ ys, r ∈ RegExp.languageOf α e
a3_right : xs ++ ys.join = w
⊢... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2_left : xs ∈ RegExp.languageOf α (RegExp.derivative a e)
ys : List (List α)
a3_left : ∀ r ∈... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp only [← ih] | α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2_left : xs ∈ RegExp.languageOf α (RegExp.derivative a e)
ys : List (List α)
a3_left : ∀ r ∈ ys, r ∈ RegExp.languageOf α e
a3_right : xs ++ ys.join = w
⊢... | α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2_left : xs ∈ RegExp.languageOf α (RegExp.derivative a e)
ys : List (List α)
a3_left : ∀ r ∈ ys, r ∈ RegExp.languageOf α e
a3_right : xs ++ ys.join = w
⊢... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2_left : xs ∈ RegExp.languageOf α (RegExp.derivative a e)
ys : List (List α)
a3_left : ∀ r ∈... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | sorry | α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2_left : xs ∈ RegExp.languageOf α (RegExp.derivative a e)
ys : List (List α)
a3_left : ∀ r ∈ ys, r ∈ RegExp.languageOf α e
a3_right : xs ++ ys.join = w
⊢... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2_left : xs ∈ RegExp.languageOf α (RegExp.derivative a e)
ys : List (List α)
a3_left : ∀ r ∈... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_imp_fastAdmitsAux | [217, 1] | [240, 10] | induction F generalizing binders | F : Formula
v u : VarName
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsAux v u binders F
⊢ fastAdmitsAux v u binders F | case pred_const_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsAux v u binders (pred_const_ a✝¹ a✝)
⊢ fastAdmitsAux v u binders (pred_const_ a✝¹ a✝)
case pred_var_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsA... | Please generate a tactic in lean4 to solve the state.
STATE:
F : Formula
v u : VarName
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsAux v u binders F
⊢ fastAdmitsAux v u binders F
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_imp_fastAdmitsAux | [217, 1] | [240, 10] | all_goals
simp only [admitsAux] at h2
simp only [fastAdmitsAux] | case pred_const_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsAux v u binders (pred_const_ a✝¹ a✝)
⊢ fastAdmitsAux v u binders (pred_const_ a✝¹ a✝)
case pred_var_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsA... | case pred_const_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
h2 : v ∈ a✝ ∧ v ∉ binders → u ∉ binders
⊢ v ∈ a✝ → u ∉ binders
case pred_var_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
h2 : v ∈ a✝ ∧ v ∉ binders → u ∉ binders
⊢ v ∈ ... | Please generate a tactic in lean4 to solve the state.
STATE:
case pred_const_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsAux v u binders (pred_const_ a✝¹ a✝)
⊢ fastAdmitsAux v u binders (pred_const_ a✝¹ a✝)
case pred_var_
v u : VarName
a✝¹ : PredName
a✝ : List V... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_imp_fastAdmitsAux | [217, 1] | [240, 10] | all_goals
tauto | case pred_const_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
h2 : v ∈ a✝ ∧ v ∉ binders → u ∉ binders
⊢ v ∈ a✝ → u ∉ binders
case pred_var_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
h2 : v ∈ a✝ ∧ v ∉ binders → u ∉ binders
⊢ v ∈ ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pred_const_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
h2 : v ∈ a✝ ∧ v ∉ binders → u ∉ binders
⊢ v ∈ a✝ → u ∉ binders
case pred_var_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_imp_fastAdmitsAux | [217, 1] | [240, 10] | simp only [admitsAux] at h2 | case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsAux v u binders (def_ a✝¹ a✝)
⊢ fastAdmitsAux v u binders (def_ a✝¹ a✝) | case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
h2 : v ∈ a✝ ∧ v ∉ binders → u ∉ binders
⊢ fastAdmitsAux v u binders (def_ a✝¹ a✝) | Please generate a tactic in lean4 to solve the state.
STATE:
case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsAux v u binders (def_ a✝¹ a✝)
⊢ fastAdmitsAux v u binders (def_ a✝¹ a✝)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_imp_fastAdmitsAux | [217, 1] | [240, 10] | simp only [fastAdmitsAux] | case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
h2 : v ∈ a✝ ∧ v ∉ binders → u ∉ binders
⊢ fastAdmitsAux v u binders (def_ a✝¹ a✝) | case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
h2 : v ∈ a✝ ∧ v ∉ binders → u ∉ binders
⊢ v ∈ a✝ → u ∉ binders | Please generate a tactic in lean4 to solve the state.
STATE:
case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
h2 : v ∈ a✝ ∧ v ∉ binders → u ∉ binders
⊢ fastAdmitsAux v u binders (def_ a✝¹ a✝)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_imp_fastAdmitsAux | [217, 1] | [240, 10] | by_cases c1 : v = x | v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → admitsAux v u binders phi → fastAdmitsAux v u binders phi
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsAux v u (binders ∪ {x}) phi
⊢ v = x ∨ fastAdmitsAux v u (binders ∪ {x}) phi | case pos
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → admitsAux v u binders phi → fastAdmitsAux v u binders phi
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsAux v u (binders ∪ {x}) phi
c1 : v = x
⊢ v = x ∨ fastAdmitsAux v u (binders ∪ {x}) phi
case neg
v u x : VarName
phi ... | Please generate a tactic in lean4 to solve the state.
STATE:
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → admitsAux v u binders phi → fastAdmitsAux v u binders phi
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsAux v u (binders ∪ {x}) phi
⊢ v = x ∨ fastAdmitsAux v u (binders ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_imp_fastAdmitsAux | [217, 1] | [240, 10] | left | case pos
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → admitsAux v u binders phi → fastAdmitsAux v u binders phi
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsAux v u (binders ∪ {x}) phi
c1 : v = x
⊢ v = x ∨ fastAdmitsAux v u (binders ∪ {x}) phi | case pos.h
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → admitsAux v u binders phi → fastAdmitsAux v u binders phi
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsAux v u (binders ∪ {x}) phi
c1 : v = x
⊢ v = x | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → admitsAux v u binders phi → fastAdmitsAux v u binders phi
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsAux v u (binders ∪ {x}) phi
c1 : v = x
⊢ v = x ∨ fastAdm... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_imp_fastAdmitsAux | [217, 1] | [240, 10] | exact c1 | case pos.h
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → admitsAux v u binders phi → fastAdmitsAux v u binders phi
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsAux v u (binders ∪ {x}) phi
c1 : v = x
⊢ v = x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.h
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → admitsAux v u binders phi → fastAdmitsAux v u binders phi
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsAux v u (binders ∪ {x}) phi
c1 : v = x
⊢ v = x
TACTIC:... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_imp_fastAdmitsAux | [217, 1] | [240, 10] | right | case neg
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → admitsAux v u binders phi → fastAdmitsAux v u binders phi
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsAux v u (binders ∪ {x}) phi
c1 : ¬v = x
⊢ v = x ∨ fastAdmitsAux v u (binders ∪ {x}) phi | case neg.h
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → admitsAux v u binders phi → fastAdmitsAux v u binders phi
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsAux v u (binders ∪ {x}) phi
c1 : ¬v = x
⊢ fastAdmitsAux v u (binders ∪ {x}) phi | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → admitsAux v u binders phi → fastAdmitsAux v u binders phi
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsAux v u (binders ∪ {x}) phi
c1 : ¬v = x
⊢ v = x ∨ fastAd... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_imp_fastAdmitsAux | [217, 1] | [240, 10] | apply phi_ih | case neg.h
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → admitsAux v u binders phi → fastAdmitsAux v u binders phi
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsAux v u (binders ∪ {x}) phi
c1 : ¬v = x
⊢ fastAdmitsAux v u (binders ∪ {x}) phi | case neg.h.h1
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → admitsAux v u binders phi → fastAdmitsAux v u binders phi
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsAux v u (binders ∪ {x}) phi
c1 : ¬v = x
⊢ v ∉ binders ∪ {x}
case neg.h.h2
v u x : VarName
phi : Formula
phi_ih ... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.h
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → admitsAux v u binders phi → fastAdmitsAux v u binders phi
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsAux v u (binders ∪ {x}) phi
c1 : ¬v = x
⊢ fastAdmitsAu... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_imp_fastAdmitsAux | [217, 1] | [240, 10] | simp | case neg.h.h1
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → admitsAux v u binders phi → fastAdmitsAux v u binders phi
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsAux v u (binders ∪ {x}) phi
c1 : ¬v = x
⊢ v ∉ binders ∪ {x} | case neg.h.h1
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → admitsAux v u binders phi → fastAdmitsAux v u binders phi
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsAux v u (binders ∪ {x}) phi
c1 : ¬v = x
⊢ v ∉ binders ∧ ¬v = x | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.h.h1
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → admitsAux v u binders phi → fastAdmitsAux v u binders phi
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsAux v u (binders ∪ {x}) phi
c1 : ¬v = x
⊢ v ∉ binde... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_imp_fastAdmitsAux | [217, 1] | [240, 10] | tauto | case neg.h.h1
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → admitsAux v u binders phi → fastAdmitsAux v u binders phi
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsAux v u (binders ∪ {x}) phi
c1 : ¬v = x
⊢ v ∉ binders ∧ ¬v = x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.h.h1
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → admitsAux v u binders phi → fastAdmitsAux v u binders phi
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsAux v u (binders ∪ {x}) phi
c1 : ¬v = x
⊢ v ∉ binde... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_imp_fastAdmitsAux | [217, 1] | [240, 10] | exact h2 | case neg.h.h2
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → admitsAux v u binders phi → fastAdmitsAux v u binders phi
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsAux v u (binders ∪ {x}) phi
c1 : ¬v = x
⊢ admitsAux v u (binders ∪ {x}) phi | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.h.h2
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → admitsAux v u binders phi → fastAdmitsAux v u binders phi
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsAux v u (binders ∪ {x}) phi
c1 : ¬v = x
⊢ admitsAux... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admitsAux_imp_fastAdmitsAux | [217, 1] | [240, 10] | tauto | case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
h2 : v ∈ a✝ ∧ v ∉ binders → u ∉ binders
⊢ v ∈ a✝ → u ∉ binders | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
h2 : v ∈ a✝ ∧ v ∉ binders → u ∉ binders
⊢ v ∈ a✝ → u ∉ binders
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.mem_binders_imp_admitsAux | [243, 1] | [259, 10] | induction F generalizing binders | F : Formula
v u : VarName
binders : Finset VarName
h1 : v ∈ binders
⊢ admitsAux v u binders F | case pred_const_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ binders
⊢ admitsAux v u binders (pred_const_ a✝¹ a✝)
case pred_var_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ binders
⊢ admitsAux v u binders (pred_var_ a✝¹ a✝)
case eq_
v u a✝¹ a✝ ... | Please generate a tactic in lean4 to solve the state.
STATE:
F : Formula
v u : VarName
binders : Finset VarName
h1 : v ∈ binders
⊢ admitsAux v u binders F
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.mem_binders_imp_admitsAux | [243, 1] | [259, 10] | all_goals
simp only [admitsAux] | case pred_const_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ binders
⊢ admitsAux v u binders (pred_const_ a✝¹ a✝)
case pred_var_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ binders
⊢ admitsAux v u binders (pred_var_ a✝¹ a✝)
case eq_
v u a✝¹ a✝ ... | case pred_const_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ binders
⊢ v ∈ a✝ ∧ v ∉ binders → u ∉ binders
case pred_var_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ binders
⊢ v ∈ a✝ ∧ v ∉ binders → u ∉ binders
case eq_
v u a✝¹ a✝ : VarName
bind... | Please generate a tactic in lean4 to solve the state.
STATE:
case pred_const_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ binders
⊢ admitsAux v u binders (pred_const_ a✝¹ a✝)
case pred_var_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ binders
⊢ a... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.mem_binders_imp_admitsAux | [243, 1] | [259, 10] | case forall_ x phi phi_ih | exists_ x phi phi_ih =>
apply phi_ih
simp
left
exact h1 | v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∈ binders → admitsAux v u binders phi
binders : Finset VarName
h1 : v ∈ binders
⊢ admitsAux v u (binders ∪ {x}) phi | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∈ binders → admitsAux v u binders phi
binders : Finset VarName
h1 : v ∈ binders
⊢ admitsAux v u (binders ∪ {x}) phi
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.mem_binders_imp_admitsAux | [243, 1] | [259, 10] | all_goals
tauto | case pred_const_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ binders
⊢ v ∈ a✝ ∧ v ∉ binders → u ∉ binders
case pred_var_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ binders
⊢ v ∈ a✝ ∧ v ∉ binders → u ∉ binders
case eq_
v u a✝¹ a✝ : VarName
bind... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pred_const_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ binders
⊢ v ∈ a✝ ∧ v ∉ binders → u ∉ binders
case pred_var_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ binders
⊢ v ∈ a✝ ∧ ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.mem_binders_imp_admitsAux | [243, 1] | [259, 10] | simp only [admitsAux] | case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ binders
⊢ admitsAux v u binders (def_ a✝¹ a✝) | case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ binders
⊢ v ∈ a✝ ∧ v ∉ binders → u ∉ binders | Please generate a tactic in lean4 to solve the state.
STATE:
case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ binders
⊢ admitsAux v u binders (def_ a✝¹ a✝)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.mem_binders_imp_admitsAux | [243, 1] | [259, 10] | apply phi_ih | v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∈ binders → admitsAux v u binders phi
binders : Finset VarName
h1 : v ∈ binders
⊢ admitsAux v u (binders ∪ {x}) phi | case h1
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∈ binders → admitsAux v u binders phi
binders : Finset VarName
h1 : v ∈ binders
⊢ v ∈ binders ∪ {x} | Please generate a tactic in lean4 to solve the state.
STATE:
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∈ binders → admitsAux v u binders phi
binders : Finset VarName
h1 : v ∈ binders
⊢ admitsAux v u (binders ∪ {x}) phi
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.mem_binders_imp_admitsAux | [243, 1] | [259, 10] | simp | case h1
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∈ binders → admitsAux v u binders phi
binders : Finset VarName
h1 : v ∈ binders
⊢ v ∈ binders ∪ {x} | case h1
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∈ binders → admitsAux v u binders phi
binders : Finset VarName
h1 : v ∈ binders
⊢ v ∈ binders ∨ v = x | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∈ binders → admitsAux v u binders phi
binders : Finset VarName
h1 : v ∈ binders
⊢ v ∈ binders ∪ {x}
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.mem_binders_imp_admitsAux | [243, 1] | [259, 10] | left | case h1
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∈ binders → admitsAux v u binders phi
binders : Finset VarName
h1 : v ∈ binders
⊢ v ∈ binders ∨ v = x | case h1.h
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∈ binders → admitsAux v u binders phi
binders : Finset VarName
h1 : v ∈ binders
⊢ v ∈ binders | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∈ binders → admitsAux v u binders phi
binders : Finset VarName
h1 : v ∈ binders
⊢ v ∈ binders ∨ v = x
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.mem_binders_imp_admitsAux | [243, 1] | [259, 10] | exact h1 | case h1.h
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∈ binders → admitsAux v u binders phi
binders : Finset VarName
h1 : v ∈ binders
⊢ v ∈ binders | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∈ binders → admitsAux v u binders phi
binders : Finset VarName
h1 : v ∈ binders
⊢ v ∈ binders
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.mem_binders_imp_admitsAux | [243, 1] | [259, 10] | tauto | case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ binders
⊢ v ∈ a✝ ∧ v ∉ binders → u ∉ binders | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ binders
⊢ v ∈ a✝ ∧ v ∉ binders → u ∉ binders
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.fastAdmitsAux_imp_admitsAux | [262, 1] | [284, 10] | induction F generalizing binders | F : Formula
v u : VarName
binders : Finset VarName
h1 : fastAdmitsAux v u binders F
⊢ admitsAux v u binders F | case pred_const_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : fastAdmitsAux v u binders (pred_const_ a✝¹ a✝)
⊢ admitsAux v u binders (pred_const_ a✝¹ a✝)
case pred_var_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : fastAdmitsAux v u binders (pred_var_ a✝¹ ... | Please generate a tactic in lean4 to solve the state.
STATE:
F : Formula
v u : VarName
binders : Finset VarName
h1 : fastAdmitsAux v u binders F
⊢ admitsAux v u binders F
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.fastAdmitsAux_imp_admitsAux | [262, 1] | [284, 10] | all_goals
simp only [fastAdmitsAux] at h1
simp only [admitsAux] | case pred_const_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : fastAdmitsAux v u binders (pred_const_ a✝¹ a✝)
⊢ admitsAux v u binders (pred_const_ a✝¹ a✝)
case pred_var_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : fastAdmitsAux v u binders (pred_var_ a✝¹ ... | case pred_const_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ a✝ → u ∉ binders
⊢ v ∈ a✝ ∧ v ∉ binders → u ∉ binders
case pred_var_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ a✝ → u ∉ binders
⊢ v ∈ a✝ ∧ v ∉ binders → u ∉ binders
case eq_
v u a✝¹... | Please generate a tactic in lean4 to solve the state.
STATE:
case pred_const_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : fastAdmitsAux v u binders (pred_const_ a✝¹ a✝)
⊢ admitsAux v u binders (pred_const_ a✝¹ a✝)
case pred_var_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.fastAdmitsAux_imp_admitsAux | [262, 1] | [284, 10] | case forall_ x phi phi_ih | exists_ x phi phi_ih =>
cases h1
case inl h1 =>
apply mem_binders_imp_admitsAux
subst h1
simp
case inr h1 =>
apply phi_ih
exact h1 | v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), fastAdmitsAux v u binders phi → admitsAux v u binders phi
binders : Finset VarName
h1 : v = x ∨ fastAdmitsAux v u (binders ∪ {x}) phi
⊢ admitsAux v u (binders ∪ {x}) phi | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), fastAdmitsAux v u binders phi → admitsAux v u binders phi
binders : Finset VarName
h1 : v = x ∨ fastAdmitsAux v u (binders ∪ {x}) phi
⊢ admitsAux v u (binders ∪ {x}) phi
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.fastAdmitsAux_imp_admitsAux | [262, 1] | [284, 10] | all_goals
tauto | case pred_const_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ a✝ → u ∉ binders
⊢ v ∈ a✝ ∧ v ∉ binders → u ∉ binders
case pred_var_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ a✝ → u ∉ binders
⊢ v ∈ a✝ ∧ v ∉ binders → u ∉ binders
case eq_
v u a✝¹... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pred_const_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ a✝ → u ∉ binders
⊢ v ∈ a✝ ∧ v ∉ binders → u ∉ binders
case pred_var_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ a✝ → u ∉ b... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.fastAdmitsAux_imp_admitsAux | [262, 1] | [284, 10] | simp only [fastAdmitsAux] at h1 | case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : fastAdmitsAux v u binders (def_ a✝¹ a✝)
⊢ admitsAux v u binders (def_ a✝¹ a✝) | case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ a✝ → u ∉ binders
⊢ admitsAux v u binders (def_ a✝¹ a✝) | Please generate a tactic in lean4 to solve the state.
STATE:
case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : fastAdmitsAux v u binders (def_ a✝¹ a✝)
⊢ admitsAux v u binders (def_ a✝¹ a✝)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.fastAdmitsAux_imp_admitsAux | [262, 1] | [284, 10] | simp only [admitsAux] | case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ a✝ → u ∉ binders
⊢ admitsAux v u binders (def_ a✝¹ a✝) | case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ a✝ → u ∉ binders
⊢ v ∈ a✝ ∧ v ∉ binders → u ∉ binders | Please generate a tactic in lean4 to solve the state.
STATE:
case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ a✝ → u ∉ binders
⊢ admitsAux v u binders (def_ a✝¹ a✝)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.fastAdmitsAux_imp_admitsAux | [262, 1] | [284, 10] | cases h1 | v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), fastAdmitsAux v u binders phi → admitsAux v u binders phi
binders : Finset VarName
h1 : v = x ∨ fastAdmitsAux v u (binders ∪ {x}) phi
⊢ admitsAux v u (binders ∪ {x}) phi | case inl
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), fastAdmitsAux v u binders phi → admitsAux v u binders phi
binders : Finset VarName
h✝ : v = x
⊢ admitsAux v u (binders ∪ {x}) phi
case inr
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), fastAdmitsAux v u binders phi → a... | Please generate a tactic in lean4 to solve the state.
STATE:
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), fastAdmitsAux v u binders phi → admitsAux v u binders phi
binders : Finset VarName
h1 : v = x ∨ fastAdmitsAux v u (binders ∪ {x}) phi
⊢ admitsAux v u (binders ∪ {x}) phi
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.fastAdmitsAux_imp_admitsAux | [262, 1] | [284, 10] | case inl h1 =>
apply mem_binders_imp_admitsAux
subst h1
simp | v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), fastAdmitsAux v u binders phi → admitsAux v u binders phi
binders : Finset VarName
h1 : v = x
⊢ admitsAux v u (binders ∪ {x}) phi | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), fastAdmitsAux v u binders phi → admitsAux v u binders phi
binders : Finset VarName
h1 : v = x
⊢ admitsAux v u (binders ∪ {x}) phi
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.fastAdmitsAux_imp_admitsAux | [262, 1] | [284, 10] | case inr h1 =>
apply phi_ih
exact h1 | v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), fastAdmitsAux v u binders phi → admitsAux v u binders phi
binders : Finset VarName
h1 : fastAdmitsAux v u (binders ∪ {x}) phi
⊢ admitsAux v u (binders ∪ {x}) phi | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), fastAdmitsAux v u binders phi → admitsAux v u binders phi
binders : Finset VarName
h1 : fastAdmitsAux v u (binders ∪ {x}) phi
⊢ admitsAux v u (binders ∪ {x}) phi
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.fastAdmitsAux_imp_admitsAux | [262, 1] | [284, 10] | apply mem_binders_imp_admitsAux | v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), fastAdmitsAux v u binders phi → admitsAux v u binders phi
binders : Finset VarName
h1 : v = x
⊢ admitsAux v u (binders ∪ {x}) phi | case h1
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), fastAdmitsAux v u binders phi → admitsAux v u binders phi
binders : Finset VarName
h1 : v = x
⊢ v ∈ binders ∪ {x} | Please generate a tactic in lean4 to solve the state.
STATE:
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), fastAdmitsAux v u binders phi → admitsAux v u binders phi
binders : Finset VarName
h1 : v = x
⊢ admitsAux v u (binders ∪ {x}) phi
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.fastAdmitsAux_imp_admitsAux | [262, 1] | [284, 10] | subst h1 | case h1
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), fastAdmitsAux v u binders phi → admitsAux v u binders phi
binders : Finset VarName
h1 : v = x
⊢ v ∈ binders ∪ {x} | case h1
v u : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), fastAdmitsAux v u binders phi → admitsAux v u binders phi
binders : Finset VarName
⊢ v ∈ binders ∪ {v} | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), fastAdmitsAux v u binders phi → admitsAux v u binders phi
binders : Finset VarName
h1 : v = x
⊢ v ∈ binders ∪ {x}
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.fastAdmitsAux_imp_admitsAux | [262, 1] | [284, 10] | simp | case h1
v u : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), fastAdmitsAux v u binders phi → admitsAux v u binders phi
binders : Finset VarName
⊢ v ∈ binders ∪ {v} | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
v u : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), fastAdmitsAux v u binders phi → admitsAux v u binders phi
binders : Finset VarName
⊢ v ∈ binders ∪ {v}
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.fastAdmitsAux_imp_admitsAux | [262, 1] | [284, 10] | apply phi_ih | v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), fastAdmitsAux v u binders phi → admitsAux v u binders phi
binders : Finset VarName
h1 : fastAdmitsAux v u (binders ∪ {x}) phi
⊢ admitsAux v u (binders ∪ {x}) phi | case h1
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), fastAdmitsAux v u binders phi → admitsAux v u binders phi
binders : Finset VarName
h1 : fastAdmitsAux v u (binders ∪ {x}) phi
⊢ fastAdmitsAux v u (binders ∪ {x}) phi | Please generate a tactic in lean4 to solve the state.
STATE:
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), fastAdmitsAux v u binders phi → admitsAux v u binders phi
binders : Finset VarName
h1 : fastAdmitsAux v u (binders ∪ {x}) phi
⊢ admitsAux v u (binders ∪ {x}) phi
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.fastAdmitsAux_imp_admitsAux | [262, 1] | [284, 10] | exact h1 | case h1
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), fastAdmitsAux v u binders phi → admitsAux v u binders phi
binders : Finset VarName
h1 : fastAdmitsAux v u (binders ∪ {x}) phi
⊢ fastAdmitsAux v u (binders ∪ {x}) phi | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
v u x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), fastAdmitsAux v u binders phi → admitsAux v u binders phi
binders : Finset VarName
h1 : fastAdmitsAux v u (binders ∪ {x}) phi
⊢ fastAdmitsAux v u (binders ∪ {x}) phi
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.fastAdmitsAux_imp_admitsAux | [262, 1] | [284, 10] | tauto | case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ a✝ → u ∉ binders
⊢ v ∈ a✝ ∧ v ∉ binders → u ∉ binders | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∈ a✝ → u ∉ binders
⊢ v ∈ a✝ ∧ v ∉ binders → u ∉ binders
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admits_iff_fastAdmits | [287, 1] | [297, 46] | simp only [admits] | F : Formula
v u : VarName
⊢ admits v u F ↔ fastAdmits v u F | F : Formula
v u : VarName
⊢ admitsAux v u ∅ F ↔ fastAdmits v u F | Please generate a tactic in lean4 to solve the state.
STATE:
F : Formula
v u : VarName
⊢ admits v u F ↔ fastAdmits v u F
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admits_iff_fastAdmits | [287, 1] | [297, 46] | simp only [fastAdmits] | F : Formula
v u : VarName
⊢ admitsAux v u ∅ F ↔ fastAdmits v u F | F : Formula
v u : VarName
⊢ admitsAux v u ∅ F ↔ fastAdmitsAux v u ∅ F | Please generate a tactic in lean4 to solve the state.
STATE:
F : Formula
v u : VarName
⊢ admitsAux v u ∅ F ↔ fastAdmits v u F
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admits_iff_fastAdmits | [287, 1] | [297, 46] | constructor | F : Formula
v u : VarName
⊢ admitsAux v u ∅ F ↔ fastAdmitsAux v u ∅ F | case mp
F : Formula
v u : VarName
⊢ admitsAux v u ∅ F → fastAdmitsAux v u ∅ F
case mpr
F : Formula
v u : VarName
⊢ fastAdmitsAux v u ∅ F → admitsAux v u ∅ F | Please generate a tactic in lean4 to solve the state.
STATE:
F : Formula
v u : VarName
⊢ admitsAux v u ∅ F ↔ fastAdmitsAux v u ∅ F
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admits_iff_fastAdmits | [287, 1] | [297, 46] | apply admitsAux_imp_fastAdmitsAux | case mp
F : Formula
v u : VarName
⊢ admitsAux v u ∅ F → fastAdmitsAux v u ∅ F | case mp.h1
F : Formula
v u : VarName
⊢ v ∉ ∅ | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
F : Formula
v u : VarName
⊢ admitsAux v u ∅ F → fastAdmitsAux v u ∅ F
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admits_iff_fastAdmits | [287, 1] | [297, 46] | simp | case mp.h1
F : Formula
v u : VarName
⊢ v ∉ ∅ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.h1
F : Formula
v u : VarName
⊢ v ∉ ∅
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.admits_iff_fastAdmits | [287, 1] | [297, 46] | exact fastAdmitsAux_imp_admitsAux F v u ∅ | case mpr
F : Formula
v u : VarName
⊢ fastAdmitsAux v u ∅ F → admitsAux v u ∅ F | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
F : Formula
v u : VarName
⊢ fastAdmitsAux v u ∅ F → admitsAux v u ∅ F
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.fastAdmitsAux_self | [302, 1] | [321, 10] | induction F generalizing binders | F : Formula
v : VarName
binders : Finset VarName
h1 : v ∉ binders
⊢ fastAdmitsAux v v binders F | case pred_const_
v : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
⊢ fastAdmitsAux v v binders (pred_const_ a✝¹ a✝)
case pred_var_
v : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
⊢ fastAdmitsAux v v binders (pred_var_ a✝¹ a✝)
case eq_
v a✝¹ a... | Please generate a tactic in lean4 to solve the state.
STATE:
F : Formula
v : VarName
binders : Finset VarName
h1 : v ∉ binders
⊢ fastAdmitsAux v v binders F
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.fastAdmitsAux_self | [302, 1] | [321, 10] | all_goals
simp only [fastAdmitsAux] | case pred_const_
v : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
⊢ fastAdmitsAux v v binders (pred_const_ a✝¹ a✝)
case pred_var_
v : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
⊢ fastAdmitsAux v v binders (pred_var_ a✝¹ a✝)
case eq_
v a✝¹ a... | case pred_const_
v : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
⊢ v ∈ a✝ → v ∉ binders
case pred_var_
v : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
⊢ v ∈ a✝ → v ∉ binders
case eq_
v a✝¹ a✝ : VarName
binders : Finset VarName
h1 : v ∉ bind... | Please generate a tactic in lean4 to solve the state.
STATE:
case pred_const_
v : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
⊢ fastAdmitsAux v v binders (pred_const_ a✝¹ a✝)
case pred_var_
v : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
⊢ f... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.fastAdmitsAux_self | [302, 1] | [321, 10] | all_goals
tauto | case pred_const_
v : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
⊢ v ∈ a✝ → v ∉ binders
case pred_var_
v : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
⊢ v ∈ a✝ → v ∉ binders
case eq_
v a✝¹ a✝ : VarName
binders : Finset VarName
h1 : v ∉ bind... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pred_const_
v : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
⊢ v ∈ a✝ → v ∉ binders
case pred_var_
v : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
⊢ v ∈ a✝ → v ∉ binders
case ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.fastAdmitsAux_self | [302, 1] | [321, 10] | simp only [fastAdmitsAux] | case def_
v : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
⊢ fastAdmitsAux v v binders (def_ a✝¹ a✝) | case def_
v : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
⊢ v ∈ a✝ → v ∉ binders | Please generate a tactic in lean4 to solve the state.
STATE:
case def_
v : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
⊢ fastAdmitsAux v v binders (def_ a✝¹ a✝)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.fastAdmitsAux_self | [302, 1] | [321, 10] | by_cases c1 : v = x | v x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → fastAdmitsAux v v binders phi
binders : Finset VarName
h1 : v ∉ binders
⊢ v = x ∨ fastAdmitsAux v v (binders ∪ {x}) phi | case pos
v x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → fastAdmitsAux v v binders phi
binders : Finset VarName
h1 : v ∉ binders
c1 : v = x
⊢ v = x ∨ fastAdmitsAux v v (binders ∪ {x}) phi
case neg
v x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → fastAdmi... | Please generate a tactic in lean4 to solve the state.
STATE:
v x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → fastAdmitsAux v v binders phi
binders : Finset VarName
h1 : v ∉ binders
⊢ v = x ∨ fastAdmitsAux v v (binders ∪ {x}) phi
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.fastAdmitsAux_self | [302, 1] | [321, 10] | left | case pos
v x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → fastAdmitsAux v v binders phi
binders : Finset VarName
h1 : v ∉ binders
c1 : v = x
⊢ v = x ∨ fastAdmitsAux v v (binders ∪ {x}) phi | case pos.h
v x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → fastAdmitsAux v v binders phi
binders : Finset VarName
h1 : v ∉ binders
c1 : v = x
⊢ v = x | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
v x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → fastAdmitsAux v v binders phi
binders : Finset VarName
h1 : v ∉ binders
c1 : v = x
⊢ v = x ∨ fastAdmitsAux v v (binders ∪ {x}) phi
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.fastAdmitsAux_self | [302, 1] | [321, 10] | exact c1 | case pos.h
v x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → fastAdmitsAux v v binders phi
binders : Finset VarName
h1 : v ∉ binders
c1 : v = x
⊢ v = x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.h
v x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → fastAdmitsAux v v binders phi
binders : Finset VarName
h1 : v ∉ binders
c1 : v = x
⊢ v = x
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.fastAdmitsAux_self | [302, 1] | [321, 10] | right | case neg
v x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → fastAdmitsAux v v binders phi
binders : Finset VarName
h1 : v ∉ binders
c1 : ¬v = x
⊢ v = x ∨ fastAdmitsAux v v (binders ∪ {x}) phi | case neg.h
v x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → fastAdmitsAux v v binders phi
binders : Finset VarName
h1 : v ∉ binders
c1 : ¬v = x
⊢ fastAdmitsAux v v (binders ∪ {x}) phi | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
v x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → fastAdmitsAux v v binders phi
binders : Finset VarName
h1 : v ∉ binders
c1 : ¬v = x
⊢ v = x ∨ fastAdmitsAux v v (binders ∪ {x}) phi
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.fastAdmitsAux_self | [302, 1] | [321, 10] | apply phi_ih | case neg.h
v x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → fastAdmitsAux v v binders phi
binders : Finset VarName
h1 : v ∉ binders
c1 : ¬v = x
⊢ fastAdmitsAux v v (binders ∪ {x}) phi | case neg.h.h1
v x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → fastAdmitsAux v v binders phi
binders : Finset VarName
h1 : v ∉ binders
c1 : ¬v = x
⊢ v ∉ binders ∪ {x} | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.h
v x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → fastAdmitsAux v v binders phi
binders : Finset VarName
h1 : v ∉ binders
c1 : ¬v = x
⊢ fastAdmitsAux v v (binders ∪ {x}) phi
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.fastAdmitsAux_self | [302, 1] | [321, 10] | simp | case neg.h.h1
v x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → fastAdmitsAux v v binders phi
binders : Finset VarName
h1 : v ∉ binders
c1 : ¬v = x
⊢ v ∉ binders ∪ {x} | case neg.h.h1
v x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → fastAdmitsAux v v binders phi
binders : Finset VarName
h1 : v ∉ binders
c1 : ¬v = x
⊢ v ∉ binders ∧ ¬v = x | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.h.h1
v x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → fastAdmitsAux v v binders phi
binders : Finset VarName
h1 : v ∉ binders
c1 : ¬v = x
⊢ v ∉ binders ∪ {x}
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.fastAdmitsAux_self | [302, 1] | [321, 10] | tauto | case neg.h.h1
v x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → fastAdmitsAux v v binders phi
binders : Finset VarName
h1 : v ∉ binders
c1 : ¬v = x
⊢ v ∉ binders ∧ ¬v = x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.h.h1
v x : VarName
phi : Formula
phi_ih : ∀ (binders : Finset VarName), v ∉ binders → fastAdmitsAux v v binders phi
binders : Finset VarName
h1 : v ∉ binders
c1 : ¬v = x
⊢ v ∉ binders ∧ ¬v = x
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.fastAdmitsAux_self | [302, 1] | [321, 10] | tauto | case def_
v : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
⊢ v ∈ a✝ → v ∉ binders | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case def_
v : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
⊢ v ∈ a✝ → v ∉ binders
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.fastAdmits_self | [324, 1] | [331, 7] | simp only [fastAdmits] | F : Formula
v : VarName
⊢ fastAdmits v v F | F : Formula
v : VarName
⊢ fastAdmitsAux v v ∅ F | Please generate a tactic in lean4 to solve the state.
STATE:
F : Formula
v : VarName
⊢ fastAdmits v v F
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.fastAdmits_self | [324, 1] | [331, 7] | apply fastAdmitsAux_self | F : Formula
v : VarName
⊢ fastAdmitsAux v v ∅ F | case h1
F : Formula
v : VarName
⊢ v ∉ ∅ | Please generate a tactic in lean4 to solve the state.
STATE:
F : Formula
v : VarName
⊢ fastAdmitsAux v v ∅ F
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.fastAdmits_self | [324, 1] | [331, 7] | simp | case h1
F : Formula
v : VarName
⊢ v ∉ ∅ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
F : Formula
v : VarName
⊢ v ∉ ∅
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.not_isFreeIn_imp_fastAdmitsAux | [335, 1] | [348, 10] | induction F generalizing binders | F : Formula
v u : VarName
binders : Finset VarName
h1 : ¬isFreeIn v F
⊢ fastAdmitsAux v u binders F | case pred_const_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : ¬isFreeIn v (pred_const_ a✝¹ a✝)
⊢ fastAdmitsAux v u binders (pred_const_ a✝¹ a✝)
case pred_var_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : ¬isFreeIn v (pred_var_ a✝¹ a✝)
⊢ fastAdmitsAux v u ... | Please generate a tactic in lean4 to solve the state.
STATE:
F : Formula
v u : VarName
binders : Finset VarName
h1 : ¬isFreeIn v F
⊢ fastAdmitsAux v u binders F
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.not_isFreeIn_imp_fastAdmitsAux | [335, 1] | [348, 10] | all_goals
simp only [isFreeIn] at h1
simp only [fastAdmitsAux] | case pred_const_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : ¬isFreeIn v (pred_const_ a✝¹ a✝)
⊢ fastAdmitsAux v u binders (pred_const_ a✝¹ a✝)
case pred_var_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : ¬isFreeIn v (pred_var_ a✝¹ a✝)
⊢ fastAdmitsAux v u ... | case pred_const_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ a✝
⊢ v ∈ a✝ → u ∉ binders
case pred_var_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ a✝
⊢ v ∈ a✝ → u ∉ binders
case eq_
v u a✝¹ a✝ : VarName
binders : Finset VarName
h1 : ¬(v = a✝¹ ∨ ... | Please generate a tactic in lean4 to solve the state.
STATE:
case pred_const_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : ¬isFreeIn v (pred_const_ a✝¹ a✝)
⊢ fastAdmitsAux v u binders (pred_const_ a✝¹ a✝)
case pred_var_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset Var... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.not_isFreeIn_imp_fastAdmitsAux | [335, 1] | [348, 10] | all_goals
tauto | case pred_const_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ a✝
⊢ v ∈ a✝ → u ∉ binders
case pred_var_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ a✝
⊢ v ∈ a✝ → u ∉ binders
case eq_
v u a✝¹ a✝ : VarName
binders : Finset VarName
h1 : ¬(v = a✝¹ ∨ ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pred_const_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ a✝
⊢ v ∈ a✝ → u ∉ binders
case pred_var_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ a✝
⊢ v ∈ a✝ → u ∉ binders
case eq_
v ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.not_isFreeIn_imp_fastAdmitsAux | [335, 1] | [348, 10] | simp only [isFreeIn] at h1 | case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : ¬isFreeIn v (def_ a✝¹ a✝)
⊢ fastAdmitsAux v u binders (def_ a✝¹ a✝) | case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ a✝
⊢ fastAdmitsAux v u binders (def_ a✝¹ a✝) | Please generate a tactic in lean4 to solve the state.
STATE:
case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : ¬isFreeIn v (def_ a✝¹ a✝)
⊢ fastAdmitsAux v u binders (def_ a✝¹ a✝)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.not_isFreeIn_imp_fastAdmitsAux | [335, 1] | [348, 10] | simp only [fastAdmitsAux] | case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ a✝
⊢ fastAdmitsAux v u binders (def_ a✝¹ a✝) | case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ a✝
⊢ v ∈ a✝ → u ∉ binders | Please generate a tactic in lean4 to solve the state.
STATE:
case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ a✝
⊢ fastAdmitsAux v u binders (def_ a✝¹ a✝)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.not_isFreeIn_imp_fastAdmitsAux | [335, 1] | [348, 10] | tauto | case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ a✝
⊢ v ∈ a✝ → u ∉ binders | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ a✝
⊢ v ∈ a✝ → u ∉ binders
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.not_isFreeIn_imp_fastAdmits | [351, 1] | [358, 50] | simp only [fastAdmits] | F : Formula
v u : VarName
h1 : ¬isFreeIn v F
⊢ fastAdmits v u F | F : Formula
v u : VarName
h1 : ¬isFreeIn v F
⊢ fastAdmitsAux v u ∅ F | Please generate a tactic in lean4 to solve the state.
STATE:
F : Formula
v u : VarName
h1 : ¬isFreeIn v F
⊢ fastAdmits v u F
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.not_isFreeIn_imp_fastAdmits | [351, 1] | [358, 50] | exact not_isFreeIn_imp_fastAdmitsAux F v u ∅ h1 | F : Formula
v u : VarName
h1 : ¬isFreeIn v F
⊢ fastAdmitsAux v u ∅ F | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
F : Formula
v u : VarName
h1 : ¬isFreeIn v F
⊢ fastAdmitsAux v u ∅ F
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/One/Rec/Admits.lean | FOL.NV.Sub.Var.One.Rec.not_isBoundIn_imp_fastAdmitsAux | [362, 1] | [385, 10] | induction F generalizing binders | F : Formula
v u : VarName
binders : Finset VarName
h1 : ¬isBoundIn u F
h2 : u ∉ binders
⊢ fastAdmitsAux v u binders F | case pred_const_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : ¬isBoundIn u (pred_const_ a✝¹ a✝)
h2 : u ∉ binders
⊢ fastAdmitsAux v u binders (pred_const_ a✝¹ a✝)
case pred_var_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : ¬isBoundIn u (pred_var_ a✝¹ a✝)
h... | Please generate a tactic in lean4 to solve the state.
STATE:
F : Formula
v u : VarName
binders : Finset VarName
h1 : ¬isBoundIn u F
h2 : u ∉ binders
⊢ fastAdmitsAux v u binders F
TACTIC:
|
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