Split (1)

train · 219k rows

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/NV/Margaris/Fol.lean	FOL.NV.Forall_spec_id'	[746, 1]	[764, 13]	simp only [Forall_] at h1	P : Formula Δ : Set Formula h1 : IsDeduct Δ (Forall_ [] P) ⊢ IsDeduct Δ P	P : Formula Δ : Set Formula h1 : IsDeduct Δ (List.foldr forall_ P []) ⊢ IsDeduct Δ P	Please generate a tactic in lean4 to solve the state. STATE: P : Formula Δ : Set Formula h1 : IsDeduct Δ (Forall_ [] P) ⊢ IsDeduct Δ P TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.Forall_spec_id'	[746, 1]	[764, 13]	simp at h1	P : Formula Δ : Set Formula h1 : IsDeduct Δ (List.foldr forall_ P []) ⊢ IsDeduct Δ P	P : Formula Δ : Set Formula h1 : IsDeduct Δ P ⊢ IsDeduct Δ P	Please generate a tactic in lean4 to solve the state. STATE: P : Formula Δ : Set Formula h1 : IsDeduct Δ (List.foldr forall_ P []) ⊢ IsDeduct Δ P TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.Forall_spec_id'	[746, 1]	[764, 13]	exact h1	P : Formula Δ : Set Formula h1 : IsDeduct Δ P ⊢ IsDeduct Δ P	no goals	Please generate a tactic in lean4 to solve the state. STATE: P : Formula Δ : Set Formula h1 : IsDeduct Δ P ⊢ IsDeduct Δ P TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.Forall_spec_id'	[746, 1]	[764, 13]	simp only [Forall_] at h1	P : Formula Δ : Set Formula xs_hd : VarName xs_tl : List VarName xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P h1 : IsDeduct Δ (Forall_ (xs_hd :: xs_tl) P) ⊢ IsDeduct Δ P	P : Formula Δ : Set Formula xs_hd : VarName xs_tl : List VarName xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P h1 : IsDeduct Δ (List.foldr forall_ P (xs_hd :: xs_tl)) ⊢ IsDeduct Δ P	Please generate a tactic in lean4 to solve the state. STATE: P : Formula Δ : Set Formula xs_hd : VarName xs_tl : List VarName xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P h1 : IsDeduct Δ (Forall_ (xs_hd :: xs_tl) P) ⊢ IsDeduct Δ P TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.Forall_spec_id'	[746, 1]	[764, 13]	simp at h1	P : Formula Δ : Set Formula xs_hd : VarName xs_tl : List VarName xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P h1 : IsDeduct Δ (List.foldr forall_ P (xs_hd :: xs_tl)) ⊢ IsDeduct Δ P	P : Formula Δ : Set Formula xs_hd : VarName xs_tl : List VarName xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P h1 : IsDeduct Δ (forall_ xs_hd (List.foldr forall_ P xs_tl)) ⊢ IsDeduct Δ P	Please generate a tactic in lean4 to solve the state. STATE: P : Formula Δ : Set Formula xs_hd : VarName xs_tl : List VarName xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P h1 : IsDeduct Δ (List.foldr forall_ P (xs_hd :: xs_tl)) ⊢ IsDeduct Δ P TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.Forall_spec_id'	[746, 1]	[764, 13]	apply xs_ih	P : Formula Δ : Set Formula xs_hd : VarName xs_tl : List VarName xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P h1 : IsDeduct Δ (forall_ xs_hd (List.foldr forall_ P xs_tl)) ⊢ IsDeduct Δ P	P : Formula Δ : Set Formula xs_hd : VarName xs_tl : List VarName xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P h1 : IsDeduct Δ (forall_ xs_hd (List.foldr forall_ P xs_tl)) ⊢ IsDeduct Δ (Forall_ xs_tl P)	Please generate a tactic in lean4 to solve the state. STATE: P : Formula Δ : Set Formula xs_hd : VarName xs_tl : List VarName xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P h1 : IsDeduct Δ (forall_ xs_hd (List.foldr forall_ P xs_tl)) ⊢ IsDeduct Δ P TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.Forall_spec_id'	[746, 1]	[764, 13]	simp only [Forall_]	P : Formula Δ : Set Formula xs_hd : VarName xs_tl : List VarName xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P h1 : IsDeduct Δ (forall_ xs_hd (List.foldr forall_ P xs_tl)) ⊢ IsDeduct Δ (Forall_ xs_tl P)	P : Formula Δ : Set Formula xs_hd : VarName xs_tl : List VarName xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P h1 : IsDeduct Δ (forall_ xs_hd (List.foldr forall_ P xs_tl)) ⊢ IsDeduct Δ (List.foldr forall_ P xs_tl)	Please generate a tactic in lean4 to solve the state. STATE: P : Formula Δ : Set Formula xs_hd : VarName xs_tl : List VarName xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P h1 : IsDeduct Δ (forall_ xs_hd (List.foldr forall_ P xs_tl)) ⊢ IsDeduct Δ (Forall_ xs_tl P) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.Forall_spec_id'	[746, 1]	[764, 13]	apply specId xs_hd	P : Formula Δ : Set Formula xs_hd : VarName xs_tl : List VarName xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P h1 : IsDeduct Δ (forall_ xs_hd (List.foldr forall_ P xs_tl)) ⊢ IsDeduct Δ (List.foldr forall_ P xs_tl)	case h1 P : Formula Δ : Set Formula xs_hd : VarName xs_tl : List VarName xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P h1 : IsDeduct Δ (forall_ xs_hd (List.foldr forall_ P xs_tl)) ⊢ IsDeduct Δ (forall_ xs_hd (List.foldr forall_ P xs_tl))	Please generate a tactic in lean4 to solve the state. STATE: P : Formula Δ : Set Formula xs_hd : VarName xs_tl : List VarName xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P h1 : IsDeduct Δ (forall_ xs_hd (List.foldr forall_ P xs_tl)) ⊢ IsDeduct Δ (List.foldr forall_ P xs_tl) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.Forall_spec_id'	[746, 1]	[764, 13]	exact h1	case h1 P : Formula Δ : Set Formula xs_hd : VarName xs_tl : List VarName xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P h1 : IsDeduct Δ (forall_ xs_hd (List.foldr forall_ P xs_tl)) ⊢ IsDeduct Δ (forall_ xs_hd (List.foldr forall_ P xs_tl))	no goals	Please generate a tactic in lean4 to solve the state. STATE: case h1 P : Formula Δ : Set Formula xs_hd : VarName xs_tl : List VarName xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P h1 : IsDeduct Δ (forall_ xs_hd (List.foldr forall_ P xs_tl)) ⊢ IsDeduct Δ (forall_ xs_hd (List.foldr forall_ P xs_tl)) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.Forall_isBoundIn	[767, 1]	[781, 10]	simp only [Formula.Forall_]	P : Formula xs : List VarName x : VarName ⊢ isBoundIn x (Forall_ xs P) ↔ x ∈ xs ∨ isBoundIn x P	P : Formula xs : List VarName x : VarName ⊢ isBoundIn x (List.foldr forall_ P xs) ↔ x ∈ xs ∨ isBoundIn x P	Please generate a tactic in lean4 to solve the state. STATE: P : Formula xs : List VarName x : VarName ⊢ isBoundIn x (Forall_ xs P) ↔ x ∈ xs ∨ isBoundIn x P TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.Forall_isBoundIn	[767, 1]	[781, 10]	induction xs	P : Formula xs : List VarName x : VarName ⊢ isBoundIn x (List.foldr forall_ P xs) ↔ x ∈ xs ∨ isBoundIn x P	case nil P : Formula x : VarName ⊢ isBoundIn x (List.foldr forall_ P []) ↔ x ∈ [] ∨ isBoundIn x P case cons P : Formula x head✝ : VarName tail✝ : List VarName tail_ih✝ : isBoundIn x (List.foldr forall_ P tail✝) ↔ x ∈ tail✝ ∨ isBoundIn x P ⊢ isBoundIn x (List.foldr forall_ P (head✝ :: tail✝)) ↔ x ∈ head✝ :: tail✝ ∨ isB...	Please generate a tactic in lean4 to solve the state. STATE: P : Formula xs : List VarName x : VarName ⊢ isBoundIn x (List.foldr forall_ P xs) ↔ x ∈ xs ∨ isBoundIn x P TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.Forall_isBoundIn	[767, 1]	[781, 10]	case nil => simp	P : Formula x : VarName ⊢ isBoundIn x (List.foldr forall_ P []) ↔ x ∈ [] ∨ isBoundIn x P	no goals	Please generate a tactic in lean4 to solve the state. STATE: P : Formula x : VarName ⊢ isBoundIn x (List.foldr forall_ P []) ↔ x ∈ [] ∨ isBoundIn x P TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.Forall_isBoundIn	[767, 1]	[781, 10]	case cons xs_hd xs_tl xs_ih => simp simp only [isBoundIn] simp only [xs_ih] tauto	P : Formula x xs_hd : VarName xs_tl : List VarName xs_ih : isBoundIn x (List.foldr forall_ P xs_tl) ↔ x ∈ xs_tl ∨ isBoundIn x P ⊢ isBoundIn x (List.foldr forall_ P (xs_hd :: xs_tl)) ↔ x ∈ xs_hd :: xs_tl ∨ isBoundIn x P	no goals	Please generate a tactic in lean4 to solve the state. STATE: P : Formula x xs_hd : VarName xs_tl : List VarName xs_ih : isBoundIn x (List.foldr forall_ P xs_tl) ↔ x ∈ xs_tl ∨ isBoundIn x P ⊢ isBoundIn x (List.foldr forall_ P (xs_hd :: xs_tl)) ↔ x ∈ xs_hd :: xs_tl ∨ isBoundIn x P TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.Forall_isBoundIn	[767, 1]	[781, 10]	simp	P : Formula x : VarName ⊢ isBoundIn x (List.foldr forall_ P []) ↔ x ∈ [] ∨ isBoundIn x P	no goals	Please generate a tactic in lean4 to solve the state. STATE: P : Formula x : VarName ⊢ isBoundIn x (List.foldr forall_ P []) ↔ x ∈ [] ∨ isBoundIn x P TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.Forall_isBoundIn	[767, 1]	[781, 10]	simp	P : Formula x xs_hd : VarName xs_tl : List VarName xs_ih : isBoundIn x (List.foldr forall_ P xs_tl) ↔ x ∈ xs_tl ∨ isBoundIn x P ⊢ isBoundIn x (List.foldr forall_ P (xs_hd :: xs_tl)) ↔ x ∈ xs_hd :: xs_tl ∨ isBoundIn x P	P : Formula x xs_hd : VarName xs_tl : List VarName xs_ih : isBoundIn x (List.foldr forall_ P xs_tl) ↔ x ∈ xs_tl ∨ isBoundIn x P ⊢ isBoundIn x (forall_ xs_hd (List.foldr forall_ P xs_tl)) ↔ (x = xs_hd ∨ x ∈ xs_tl) ∨ isBoundIn x P	Please generate a tactic in lean4 to solve the state. STATE: P : Formula x xs_hd : VarName xs_tl : List VarName xs_ih : isBoundIn x (List.foldr forall_ P xs_tl) ↔ x ∈ xs_tl ∨ isBoundIn x P ⊢ isBoundIn x (List.foldr forall_ P (xs_hd :: xs_tl)) ↔ x ∈ xs_hd :: xs_tl ∨ isBoundIn x P TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.Forall_isBoundIn	[767, 1]	[781, 10]	simp only [isBoundIn]	P : Formula x xs_hd : VarName xs_tl : List VarName xs_ih : isBoundIn x (List.foldr forall_ P xs_tl) ↔ x ∈ xs_tl ∨ isBoundIn x P ⊢ isBoundIn x (forall_ xs_hd (List.foldr forall_ P xs_tl)) ↔ (x = xs_hd ∨ x ∈ xs_tl) ∨ isBoundIn x P	P : Formula x xs_hd : VarName xs_tl : List VarName xs_ih : isBoundIn x (List.foldr forall_ P xs_tl) ↔ x ∈ xs_tl ∨ isBoundIn x P ⊢ x = xs_hd ∨ isBoundIn x (List.foldr forall_ P xs_tl) ↔ (x = xs_hd ∨ x ∈ xs_tl) ∨ isBoundIn x P	Please generate a tactic in lean4 to solve the state. STATE: P : Formula x xs_hd : VarName xs_tl : List VarName xs_ih : isBoundIn x (List.foldr forall_ P xs_tl) ↔ x ∈ xs_tl ∨ isBoundIn x P ⊢ isBoundIn x (forall_ xs_hd (List.foldr forall_ P xs_tl)) ↔ (x = xs_hd ∨ x ∈ xs_tl) ∨ isBoundIn x P TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.Forall_isBoundIn	[767, 1]	[781, 10]	simp only [xs_ih]	P : Formula x xs_hd : VarName xs_tl : List VarName xs_ih : isBoundIn x (List.foldr forall_ P xs_tl) ↔ x ∈ xs_tl ∨ isBoundIn x P ⊢ x = xs_hd ∨ isBoundIn x (List.foldr forall_ P xs_tl) ↔ (x = xs_hd ∨ x ∈ xs_tl) ∨ isBoundIn x P	P : Formula x xs_hd : VarName xs_tl : List VarName xs_ih : isBoundIn x (List.foldr forall_ P xs_tl) ↔ x ∈ xs_tl ∨ isBoundIn x P ⊢ x = xs_hd ∨ x ∈ xs_tl ∨ isBoundIn x P ↔ (x = xs_hd ∨ x ∈ xs_tl) ∨ isBoundIn x P	Please generate a tactic in lean4 to solve the state. STATE: P : Formula x xs_hd : VarName xs_tl : List VarName xs_ih : isBoundIn x (List.foldr forall_ P xs_tl) ↔ x ∈ xs_tl ∨ isBoundIn x P ⊢ x = xs_hd ∨ isBoundIn x (List.foldr forall_ P xs_tl) ↔ (x = xs_hd ∨ x ∈ xs_tl) ∨ isBoundIn x P TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.Forall_isBoundIn	[767, 1]	[781, 10]	tauto	P : Formula x xs_hd : VarName xs_tl : List VarName xs_ih : isBoundIn x (List.foldr forall_ P xs_tl) ↔ x ∈ xs_tl ∨ isBoundIn x P ⊢ x = xs_hd ∨ x ∈ xs_tl ∨ isBoundIn x P ↔ (x = xs_hd ∨ x ∈ xs_tl) ∨ isBoundIn x P	no goals	Please generate a tactic in lean4 to solve the state. STATE: P : Formula x xs_hd : VarName xs_tl : List VarName xs_ih : isBoundIn x (List.foldr forall_ P xs_tl) ↔ x ∈ xs_tl ∨ isBoundIn x P ⊢ x = xs_hd ∨ x ∈ xs_tl ∨ isBoundIn x P ↔ (x = xs_hd ∨ x ∈ xs_tl) ∨ isBoundIn x P TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.Forall_isFreeIn	[784, 1]	[798, 10]	simp only [Formula.Forall_]	P : Formula xs : List VarName x : VarName ⊢ isFreeIn x (Forall_ xs P) ↔ x ∉ xs ∧ isFreeIn x P	P : Formula xs : List VarName x : VarName ⊢ isFreeIn x (List.foldr forall_ P xs) ↔ x ∉ xs ∧ isFreeIn x P	Please generate a tactic in lean4 to solve the state. STATE: P : Formula xs : List VarName x : VarName ⊢ isFreeIn x (Forall_ xs P) ↔ x ∉ xs ∧ isFreeIn x P TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.Forall_isFreeIn	[784, 1]	[798, 10]	induction xs	P : Formula xs : List VarName x : VarName ⊢ isFreeIn x (List.foldr forall_ P xs) ↔ x ∉ xs ∧ isFreeIn x P	case nil P : Formula x : VarName ⊢ isFreeIn x (List.foldr forall_ P []) ↔ x ∉ [] ∧ isFreeIn x P case cons P : Formula x head✝ : VarName tail✝ : List VarName tail_ih✝ : isFreeIn x (List.foldr forall_ P tail✝) ↔ x ∉ tail✝ ∧ isFreeIn x P ⊢ isFreeIn x (List.foldr forall_ P (head✝ :: tail✝)) ↔ x ∉ head✝ :: tail✝ ∧ isFreeIn...	Please generate a tactic in lean4 to solve the state. STATE: P : Formula xs : List VarName x : VarName ⊢ isFreeIn x (List.foldr forall_ P xs) ↔ x ∉ xs ∧ isFreeIn x P TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.Forall_isFreeIn	[784, 1]	[798, 10]	case nil => simp	P : Formula x : VarName ⊢ isFreeIn x (List.foldr forall_ P []) ↔ x ∉ [] ∧ isFreeIn x P	no goals	Please generate a tactic in lean4 to solve the state. STATE: P : Formula x : VarName ⊢ isFreeIn x (List.foldr forall_ P []) ↔ x ∉ [] ∧ isFreeIn x P TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.Forall_isFreeIn	[784, 1]	[798, 10]	case cons xs_hd xs_tl xs_ih => simp simp only [isFreeIn] simp only [xs_ih] tauto	P : Formula x xs_hd : VarName xs_tl : List VarName xs_ih : isFreeIn x (List.foldr forall_ P xs_tl) ↔ x ∉ xs_tl ∧ isFreeIn x P ⊢ isFreeIn x (List.foldr forall_ P (xs_hd :: xs_tl)) ↔ x ∉ xs_hd :: xs_tl ∧ isFreeIn x P	no goals	Please generate a tactic in lean4 to solve the state. STATE: P : Formula x xs_hd : VarName xs_tl : List VarName xs_ih : isFreeIn x (List.foldr forall_ P xs_tl) ↔ x ∉ xs_tl ∧ isFreeIn x P ⊢ isFreeIn x (List.foldr forall_ P (xs_hd :: xs_tl)) ↔ x ∉ xs_hd :: xs_tl ∧ isFreeIn x P TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.Forall_isFreeIn	[784, 1]	[798, 10]	simp	P : Formula x : VarName ⊢ isFreeIn x (List.foldr forall_ P []) ↔ x ∉ [] ∧ isFreeIn x P	no goals	Please generate a tactic in lean4 to solve the state. STATE: P : Formula x : VarName ⊢ isFreeIn x (List.foldr forall_ P []) ↔ x ∉ [] ∧ isFreeIn x P TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.Forall_isFreeIn	[784, 1]	[798, 10]	simp	P : Formula x xs_hd : VarName xs_tl : List VarName xs_ih : isFreeIn x (List.foldr forall_ P xs_tl) ↔ x ∉ xs_tl ∧ isFreeIn x P ⊢ isFreeIn x (List.foldr forall_ P (xs_hd :: xs_tl)) ↔ x ∉ xs_hd :: xs_tl ∧ isFreeIn x P	P : Formula x xs_hd : VarName xs_tl : List VarName xs_ih : isFreeIn x (List.foldr forall_ P xs_tl) ↔ x ∉ xs_tl ∧ isFreeIn x P ⊢ isFreeIn x (forall_ xs_hd (List.foldr forall_ P xs_tl)) ↔ (¬x = xs_hd ∧ x ∉ xs_tl) ∧ isFreeIn x P	Please generate a tactic in lean4 to solve the state. STATE: P : Formula x xs_hd : VarName xs_tl : List VarName xs_ih : isFreeIn x (List.foldr forall_ P xs_tl) ↔ x ∉ xs_tl ∧ isFreeIn x P ⊢ isFreeIn x (List.foldr forall_ P (xs_hd :: xs_tl)) ↔ x ∉ xs_hd :: xs_tl ∧ isFreeIn x P TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.Forall_isFreeIn	[784, 1]	[798, 10]	simp only [isFreeIn]	P : Formula x xs_hd : VarName xs_tl : List VarName xs_ih : isFreeIn x (List.foldr forall_ P xs_tl) ↔ x ∉ xs_tl ∧ isFreeIn x P ⊢ isFreeIn x (forall_ xs_hd (List.foldr forall_ P xs_tl)) ↔ (¬x = xs_hd ∧ x ∉ xs_tl) ∧ isFreeIn x P	P : Formula x xs_hd : VarName xs_tl : List VarName xs_ih : isFreeIn x (List.foldr forall_ P xs_tl) ↔ x ∉ xs_tl ∧ isFreeIn x P ⊢ ¬x = xs_hd ∧ isFreeIn x (List.foldr forall_ P xs_tl) ↔ (¬x = xs_hd ∧ x ∉ xs_tl) ∧ isFreeIn x P	Please generate a tactic in lean4 to solve the state. STATE: P : Formula x xs_hd : VarName xs_tl : List VarName xs_ih : isFreeIn x (List.foldr forall_ P xs_tl) ↔ x ∉ xs_tl ∧ isFreeIn x P ⊢ isFreeIn x (forall_ xs_hd (List.foldr forall_ P xs_tl)) ↔ (¬x = xs_hd ∧ x ∉ xs_tl) ∧ isFreeIn x P TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.Forall_isFreeIn	[784, 1]	[798, 10]	simp only [xs_ih]	P : Formula x xs_hd : VarName xs_tl : List VarName xs_ih : isFreeIn x (List.foldr forall_ P xs_tl) ↔ x ∉ xs_tl ∧ isFreeIn x P ⊢ ¬x = xs_hd ∧ isFreeIn x (List.foldr forall_ P xs_tl) ↔ (¬x = xs_hd ∧ x ∉ xs_tl) ∧ isFreeIn x P	P : Formula x xs_hd : VarName xs_tl : List VarName xs_ih : isFreeIn x (List.foldr forall_ P xs_tl) ↔ x ∉ xs_tl ∧ isFreeIn x P ⊢ ¬x = xs_hd ∧ x ∉ xs_tl ∧ isFreeIn x P ↔ (¬x = xs_hd ∧ x ∉ xs_tl) ∧ isFreeIn x P	Please generate a tactic in lean4 to solve the state. STATE: P : Formula x xs_hd : VarName xs_tl : List VarName xs_ih : isFreeIn x (List.foldr forall_ P xs_tl) ↔ x ∉ xs_tl ∧ isFreeIn x P ⊢ ¬x = xs_hd ∧ isFreeIn x (List.foldr forall_ P xs_tl) ↔ (¬x = xs_hd ∧ x ∉ xs_tl) ∧ isFreeIn x P TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.Forall_isFreeIn	[784, 1]	[798, 10]	tauto	P : Formula x xs_hd : VarName xs_tl : List VarName xs_ih : isFreeIn x (List.foldr forall_ P xs_tl) ↔ x ∉ xs_tl ∧ isFreeIn x P ⊢ ¬x = xs_hd ∧ x ∉ xs_tl ∧ isFreeIn x P ↔ (¬x = xs_hd ∧ x ∉ xs_tl) ∧ isFreeIn x P	no goals	Please generate a tactic in lean4 to solve the state. STATE: P : Formula x xs_hd : VarName xs_tl : List VarName xs_ih : isFreeIn x (List.foldr forall_ P xs_tl) ↔ x ∉ xs_tl ∧ isFreeIn x P ⊢ ¬x = xs_hd ∧ x ∉ xs_tl ∧ isFreeIn x P ↔ (¬x = xs_hd ∧ x ∉ xs_tl) ∧ isFreeIn x P TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	induction h1	U V P_U P_V : Formula l : List VarName h1 : IsReplOfFormulaInFormula U V P_U P_V h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v P_U → v ∈ l ⊢ IsProof ((Forall_ l (U.iff_ V)).imp_ (P_U.iff_ P_V))	case same_ U V P_U P_V : Formula l : List VarName P_u✝ P_v✝ : Formula a✝ : P_u✝ = P_v✝ h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v P_u✝ → v ∈ l ⊢ IsProof ((Forall_ l (U.iff_ V)).imp_ (P_u✝.iff_ P_v✝)) case diff_ U V P_U P_V : Formula l : List VarName P_u✝ P_v✝ : Formula a✝¹ : P_u✝ = U a✝ : P_v✝ =...	Please generate a tactic in lean4 to solve the state. STATE: U V P_U P_V : Formula l : List VarName h1 : IsReplOfFormulaInFormula U V P_U P_V h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v P_U → v ∈ l ⊢ IsProof ((Forall_ l (U.iff_ V)).imp_ (P_U.iff_ P_V)) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	case same_ h1_P h1_P' h1_1 => subst h1_1 simp only [def_iff_] simp only [def_and_] SC	U V P_U P_V : Formula l : List VarName h1_P h1_P' : Formula h1_1 : h1_P = h1_P' h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l ⊢ IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))	no goals	Please generate a tactic in lean4 to solve the state. STATE: U V P_U P_V : Formula l : List VarName h1_P h1_P' : Formula h1_1 : h1_P = h1_P' h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l ⊢ IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	case diff_ h1_P h1_P' h1_1 h1_2 => subst h1_1 subst h1_2 apply Forall_spec_id	U V P_U P_V : Formula l : List VarName h1_P h1_P' : Formula h1_1 : h1_P = U h1_2 : h1_P' = V h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l ⊢ IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))	no goals	Please generate a tactic in lean4 to solve the state. STATE: U V P_U P_V : Formula l : List VarName h1_P h1_P' : Formula h1_1 : h1_P = U h1_2 : h1_P' = V h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l ⊢ IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	all_goals sorry	case and_ U V P_U P_V : Formula l : List VarName P_u✝ Q_u✝ P_v✝ Q_v✝ : Formula a✝¹ : IsReplOfFormulaInFormula U V P_u✝ P_v✝ a✝ : IsReplOfFormulaInFormula U V Q_u✝ Q_v✝ a_ih✝¹ : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v P_u✝ → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (P_u✝.iff_ P_v✝)) a_ih...	no goals	Please generate a tactic in lean4 to solve the state. STATE: case and_ U V P_U P_V : Formula l : List VarName P_u✝ Q_u✝ P_v✝ Q_v✝ : Formula a✝¹ : IsReplOfFormulaInFormula U V P_u✝ P_v✝ a✝ : IsReplOfFormulaInFormula U V Q_u✝ Q_v✝ a_ih✝¹ : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v P_u✝ → v ∈ l) → ...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	subst h1_1	U V P_U P_V : Formula l : List VarName h1_P h1_P' : Formula h1_1 : h1_P = h1_P' h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l ⊢ IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))	U V P_U P_V : Formula l : List VarName h1_P : Formula h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l ⊢ IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P))	Please generate a tactic in lean4 to solve the state. STATE: U V P_U P_V : Formula l : List VarName h1_P h1_P' : Formula h1_1 : h1_P = h1_P' h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l ⊢ IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	simp only [def_iff_]	U V P_U P_V : Formula l : List VarName h1_P : Formula h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l ⊢ IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P))	U V P_U P_V : Formula l : List VarName h1_P : Formula h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l ⊢ IsProof ((Forall_ l ((U.imp_ V).and_ (V.imp_ U))).imp_ ((h1_P.imp_ h1_P).and_ (h1_P.imp_ h1_P)))	Please generate a tactic in lean4 to solve the state. STATE: U V P_U P_V : Formula l : List VarName h1_P : Formula h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l ⊢ IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P)) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	simp only [def_and_]	U V P_U P_V : Formula l : List VarName h1_P : Formula h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l ⊢ IsProof ((Forall_ l ((U.imp_ V).and_ (V.imp_ U))).imp_ ((h1_P.imp_ h1_P).and_ (h1_P.imp_ h1_P)))	U V P_U P_V : Formula l : List VarName h1_P : Formula h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l ⊢ IsProof ((Forall_ l ((U.imp_ V).imp_ (V.imp_ U).not_).not_).imp_ ((h1_P.imp_ h1_P).imp_ (h1_P.imp_ h1_P).not_).not_)	Please generate a tactic in lean4 to solve the state. STATE: U V P_U P_V : Formula l : List VarName h1_P : Formula h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l ⊢ IsProof ((Forall_ l ((U.imp_ V).and_ (V.imp_ U))).imp_ ((h1_P.imp_ h1_P).and_ (h1_P.imp_ h1_P))) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	SC	U V P_U P_V : Formula l : List VarName h1_P : Formula h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l ⊢ IsProof ((Forall_ l ((U.imp_ V).imp_ (V.imp_ U).not_).not_).imp_ ((h1_P.imp_ h1_P).imp_ (h1_P.imp_ h1_P).not_).not_)	no goals	Please generate a tactic in lean4 to solve the state. STATE: U V P_U P_V : Formula l : List VarName h1_P : Formula h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l ⊢ IsProof ((Forall_ l ((U.imp_ V).imp_ (V.imp_ U).not_).not_).imp_ ((h1_P.imp_ h1_P).imp_ (h1_P.imp_ h1_P).not_).not_) TACTIC:...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	subst h1_1	U V P_U P_V : Formula l : List VarName h1_P h1_P' : Formula h1_1 : h1_P = U h1_2 : h1_P' = V h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l ⊢ IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))	V P_U P_V : Formula l : List VarName h1_P h1_P' : Formula h1_2 : h1_P' = V h2 : ∀ (v : VarName), (isFreeIn v h1_P ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l ⊢ IsProof ((Forall_ l (h1_P.iff_ V)).imp_ (h1_P.iff_ h1_P'))	Please generate a tactic in lean4 to solve the state. STATE: U V P_U P_V : Formula l : List VarName h1_P h1_P' : Formula h1_1 : h1_P = U h1_2 : h1_P' = V h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l ⊢ IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	subst h1_2	V P_U P_V : Formula l : List VarName h1_P h1_P' : Formula h1_2 : h1_P' = V h2 : ∀ (v : VarName), (isFreeIn v h1_P ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l ⊢ IsProof ((Forall_ l (h1_P.iff_ V)).imp_ (h1_P.iff_ h1_P'))	P_U P_V : Formula l : List VarName h1_P h1_P' : Formula h2 : ∀ (v : VarName), (isFreeIn v h1_P ∨ isFreeIn v h1_P') ∧ isBoundIn v h1_P → v ∈ l ⊢ IsProof ((Forall_ l (h1_P.iff_ h1_P')).imp_ (h1_P.iff_ h1_P'))	Please generate a tactic in lean4 to solve the state. STATE: V P_U P_V : Formula l : List VarName h1_P h1_P' : Formula h1_2 : h1_P' = V h2 : ∀ (v : VarName), (isFreeIn v h1_P ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l ⊢ IsProof ((Forall_ l (h1_P.iff_ V)).imp_ (h1_P.iff_ h1_P')) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	apply Forall_spec_id	P_U P_V : Formula l : List VarName h1_P h1_P' : Formula h2 : ∀ (v : VarName), (isFreeIn v h1_P ∨ isFreeIn v h1_P') ∧ isBoundIn v h1_P → v ∈ l ⊢ IsProof ((Forall_ l (h1_P.iff_ h1_P')).imp_ (h1_P.iff_ h1_P'))	no goals	Please generate a tactic in lean4 to solve the state. STATE: P_U P_V : Formula l : List VarName h1_P h1_P' : Formula h2 : ∀ (v : VarName), (isFreeIn v h1_P ∨ isFreeIn v h1_P') ∧ isBoundIn v h1_P → v ∈ l ⊢ IsProof ((Forall_ l (h1_P.iff_ h1_P')).imp_ (h1_P.iff_ h1_P')) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	simp only [isBoundIn] at h2	U V P_U P_V : Formula l : List VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v...	U V P_U P_V : Formula l : List VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v...	Please generate a tactic in lean4 to solve the state. STATE: U V P_U P_V : Formula l : List VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 :...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	apply IsDeduct.mp_ ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))	U V P_U P_V : Formula l : List VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v...	case a U V P_U P_V : Formula l : List VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBo...	Please generate a tactic in lean4 to solve the state. STATE: U V P_U P_V : Formula l : List VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 :...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	simp only [def_iff_]	case a U V P_U P_V : Formula l : List VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBo...	case a U V P_U P_V : Formula l : List VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBo...	Please generate a tactic in lean4 to solve the state. STATE: case a U V P_U P_V : Formula l : List VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	simp only [def_and_]	case a U V P_U P_V : Formula l : List VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBo...	case a U V P_U P_V : Formula l : List VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBo...	Please generate a tactic in lean4 to solve the state. STATE: case a U V P_U P_V : Formula l : List VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	SC	case a U V P_U P_V : Formula l : List VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBo...	no goals	Please generate a tactic in lean4 to solve the state. STATE: case a U V P_U P_V : Formula l : List VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	exact h1_ih h2	case a U V P_U P_V : Formula l : List VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBo...	no goals	Please generate a tactic in lean4 to solve the state. STATE: case a U V P_U P_V : Formula l : List VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	simp only [isBoundIn] at h2	U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h1_ih...	U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h1_ih...	Please generate a tactic in lean4 to solve the state. STATE: U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → ...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	apply IsDeduct.mp_ ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))	U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h1_ih...	case a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')...	Please generate a tactic in lean4 to solve the state. STATE: U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → ...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	apply IsDeduct.mp_ ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))	case a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')...	case a.a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P...	Please generate a tactic in lean4 to solve the state. STATE: case a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l)...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	simp only [def_iff_]	case a.a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P...	case a.a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P...	Please generate a tactic in lean4 to solve the state. STATE: case a.a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ ...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	simp only [def_and_]	case a.a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P...	case a.a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P...	Please generate a tactic in lean4 to solve the state. STATE: case a.a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ ...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	SC	case a.a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P...	no goals	Please generate a tactic in lean4 to solve the state. STATE: case a.a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ ...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	apply h1_ih_2	case a.a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P...	case a.a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P...	Please generate a tactic in lean4 to solve the state. STATE: case a.a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ ...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	intro v a2	case a.a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P...	case a.a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P...	Please generate a tactic in lean4 to solve the state. STATE: case a.a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ ...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	apply h2 v	case a.a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P...	case a.a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P...	Please generate a tactic in lean4 to solve the state. STATE: case a.a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ ...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	tauto	case a.a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P...	no goals	Please generate a tactic in lean4 to solve the state. STATE: case a.a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ ...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	apply h1_ih_1	case a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')...	case a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')...	Please generate a tactic in lean4 to solve the state. STATE: case a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l)...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	intro v a1	case a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')...	case a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')...	Please generate a tactic in lean4 to solve the state. STATE: case a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l)...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	apply h2 v	case a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')...	case a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')...	Please generate a tactic in lean4 to solve the state. STATE: case a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l)...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	cases a1	case a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')...	case a.intro U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ ...	Please generate a tactic in lean4 to solve the state. STATE: case a U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l)...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	constructor	U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h1_ih...	case left U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_...	Please generate a tactic in lean4 to solve the state. STATE: U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → ...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	exact a1_left	case left U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_...	no goals	Please generate a tactic in lean4 to solve the state. STATE: case left U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	left	case right U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1...	case right.h U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ ...	Please generate a tactic in lean4 to solve the state. STATE: case right U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	exact a1_right	case right.h U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ ...	no goals	Please generate a tactic in lean4 to solve the state. STATE: case right.h U V P_U P_V : Formula l : List VarName h1_P h1_Q h1_P' h1_Q' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q' h1_ih_1 : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → ...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	simp only [isBoundIn] at h2	U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V...	U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V...	Please generate a tactic in lean4 to solve the state. STATE: U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.if...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	simp at h2	U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V...	U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ isFreeIn v V ...	Please generate a tactic in lean4 to solve the state. STATE: U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.if...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	apply deduction_theorem	U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ isFreeIn v V ...	case h1 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ isFre...	Please generate a tactic in lean4 to solve the state. STATE: U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.if...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	simp	case h1 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ isFre...	case h1 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ isFre...	Please generate a tactic in lean4 to solve the state. STATE: case h1 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ ...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	apply IsDeduct.mp_ (forall_ h1_x (h1_P.iff_ h1_P'))	case h1 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ isFre...	case h1.a U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ isF...	Please generate a tactic in lean4 to solve the state. STATE: case h1 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ ...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	apply proof_imp_deduct	case h1.a U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ isF...	case h1.a.h1 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ ...	Please generate a tactic in lean4 to solve the state. STATE: case h1.a U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	apply T_18_1	case h1.a.h1 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ ...	no goals	Please generate a tactic in lean4 to solve the state. STATE: case h1.a.h1 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V))....
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	apply generalization	case h1.a U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ isF...	case h1.a.h1 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ ...	Please generate a tactic in lean4 to solve the state. STATE: case h1.a U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	apply IsDeduct.mp_ (Forall_ l (U.iff_ V))	case h1.a.h1 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ ...	case h1.a.h1.a U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ...	Please generate a tactic in lean4 to solve the state. STATE: case h1.a.h1 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V))....
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	apply proof_imp_deduct	case h1.a.h1.a U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ...	case h1.a.h1.a.h1 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v...	Please generate a tactic in lean4 to solve the state. STATE: case h1.a.h1.a U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	apply h1_ih	case h1.a.h1.a.h1 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v...	case h1.a.h1.a.h1 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v...	Please generate a tactic in lean4 to solve the state. STATE: case h1.a.h1.a.h1 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	intro v a1	case h1.a.h1.a.h1 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v...	case h1.a.h1.a.h1 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v...	Please generate a tactic in lean4 to solve the state. STATE: case h1.a.h1.a.h1 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	cases a1	case h1.a.h1.a.h1 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v...	case h1.a.h1.a.h1.intro U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFr...	Please generate a tactic in lean4 to solve the state. STATE: case h1.a.h1.a.h1 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	case _ a1_left a1_right => apply h2 v a1_left right apply a1_right	U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ isFreeIn v V ...	no goals	Please generate a tactic in lean4 to solve the state. STATE: U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.if...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	apply h2 v a1_left	U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ isFreeIn v V ...	U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ isFreeIn v V ...	Please generate a tactic in lean4 to solve the state. STATE: U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.if...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	right	U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ isFreeIn v V ...	case h U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ isFree...	Please generate a tactic in lean4 to solve the state. STATE: U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.if...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	apply a1_right	case h U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ isFree...	no goals	Please generate a tactic in lean4 to solve the state. STATE: case h U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	apply IsDeduct.assume_	case h1.a.h1.a U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ...	case h1.a.h1.a.a U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v ...	Please generate a tactic in lean4 to solve the state. STATE: case h1.a.h1.a U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	simp	case h1.a.h1.a.a U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v ...	no goals	Please generate a tactic in lean4 to solve the state. STATE: case h1.a.h1.a.a U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ ...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	intro H a1	case h1.a.h2 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ ...	case h1.a.h2 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ ...	Please generate a tactic in lean4 to solve the state. STATE: case h1.a.h2 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V))....
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	simp at a1	case h1.a.h2 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ ...	case h1.a.h2 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ ...	Please generate a tactic in lean4 to solve the state. STATE: case h1.a.h2 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V))....
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	subst a1	case h1.a.h2 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ ...	case h1.a.h2 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ ...	Please generate a tactic in lean4 to solve the state. STATE: case h1.a.h2 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V))....
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	simp only [Forall_isFreeIn]	case h1.a.h2 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ ...	case h1.a.h2 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ ...	Please generate a tactic in lean4 to solve the state. STATE: case h1.a.h2 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V))....
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	simp only [def_iff_]	case h1.a.h2 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ ...	case h1.a.h2 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ ...	Please generate a tactic in lean4 to solve the state. STATE: case h1.a.h2 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V))....
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	simp only [def_and_]	case h1.a.h2 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ ...	case h1.a.h2 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ ...	Please generate a tactic in lean4 to solve the state. STATE: case h1.a.h2 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V))....
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	simp only [isFreeIn]	case h1.a.h2 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ ...	case h1.a.h2 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ ...	Please generate a tactic in lean4 to solve the state. STATE: case h1.a.h2 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V))....
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	sorry	case h1.a.h2 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) h2 : ∀ (v : VarName), isFreeIn v U ∨ ...	no goals	Please generate a tactic in lean4 to solve the state. STATE: case h1.a.h2 U V P_U P_V : Formula l : List VarName h1_x : VarName h1_P h1_P' : Formula h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P' h1_ih : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) → IsProof ((Forall_ l (U.iff_ V))....
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.T_18_2	[802, 1]	[886, 10]	sorry	case exists_ U V P_U P_V : Formula l : List VarName x✝ : VarName P_u✝ P_v✝ : Formula a✝ : IsReplOfFormulaInFormula U V P_u✝ P_v✝ a_ih✝ : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v P_u✝ → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (P_u✝.iff_ P_v✝)) h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFree...	no goals	Please generate a tactic in lean4 to solve the state. STATE: case exists_ U V P_U P_V : Formula l : List VarName x✝ : VarName P_u✝ P_v✝ : Formula a✝ : IsReplOfFormulaInFormula U V P_u✝ P_v✝ a_ih✝ : (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v P_u✝ → v ∈ l) → IsProof ((Forall_ l (U.iff_ V)).imp_ (...
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.C_18_3	[889, 1]	[913, 13]	apply IsDeduct.mp_ (Forall_ ((U.freeVarSet ∪ V.freeVarSet) ∩ P_U.boundVarSet).toList (U.iff_ V))	U V P_U P_V : Formula h1 : IsReplOfFormulaInFormula U V P_U P_V h2 : IsProof (U.iff_ V) ⊢ IsProof (P_U.iff_ P_V)	case a U V P_U P_V : Formula h1 : IsReplOfFormulaInFormula U V P_U P_V h2 : IsProof (U.iff_ V) ⊢ IsDeduct ∅ ((Forall_ ((U.freeVarSet ∪ V.freeVarSet) ∩ P_U.boundVarSet).toList (U.iff_ V)).imp_ (P_U.iff_ P_V)) case a U V P_U P_V : Formula h1 : IsReplOfFormulaInFormula U V P_U P_V h2 : IsProof (U.iff_ V) ⊢ IsDeduct ∅ (Fo...	Please generate a tactic in lean4 to solve the state. STATE: U V P_U P_V : Formula h1 : IsReplOfFormulaInFormula U V P_U P_V h2 : IsProof (U.iff_ V) ⊢ IsProof (P_U.iff_ P_V) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.C_18_3	[889, 1]	[913, 13]	apply T_18_2 U V P_U P_V ((U.freeVarSet ∪ V.freeVarSet) ∩ P_U.boundVarSet).toList h1	case a U V P_U P_V : Formula h1 : IsReplOfFormulaInFormula U V P_U P_V h2 : IsProof (U.iff_ V) ⊢ IsDeduct ∅ ((Forall_ ((U.freeVarSet ∪ V.freeVarSet) ∩ P_U.boundVarSet).toList (U.iff_ V)).imp_ (P_U.iff_ P_V))	case a U V P_U P_V : Formula h1 : IsReplOfFormulaInFormula U V P_U P_V h2 : IsProof (U.iff_ V) ⊢ ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v P_U → v ∈ ((U.freeVarSet ∪ V.freeVarSet) ∩ P_U.boundVarSet).toList	Please generate a tactic in lean4 to solve the state. STATE: case a U V P_U P_V : Formula h1 : IsReplOfFormulaInFormula U V P_U P_V h2 : IsProof (U.iff_ V) ⊢ IsDeduct ∅ ((Forall_ ((U.freeVarSet ∪ V.freeVarSet) ∩ P_U.boundVarSet).toList (U.iff_ V)).imp_ (P_U.iff_ P_V)) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.C_18_3	[889, 1]	[913, 13]	intro v a1	case a U V P_U P_V : Formula h1 : IsReplOfFormulaInFormula U V P_U P_V h2 : IsProof (U.iff_ V) ⊢ ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v P_U → v ∈ ((U.freeVarSet ∪ V.freeVarSet) ∩ P_U.boundVarSet).toList	case a U V P_U P_V : Formula h1 : IsReplOfFormulaInFormula U V P_U P_V h2 : IsProof (U.iff_ V) v : VarName a1 : (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v P_U ⊢ v ∈ ((U.freeVarSet ∪ V.freeVarSet) ∩ P_U.boundVarSet).toList	Please generate a tactic in lean4 to solve the state. STATE: case a U V P_U P_V : Formula h1 : IsReplOfFormulaInFormula U V P_U P_V h2 : IsProof (U.iff_ V) ⊢ ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v P_U → v ∈ ((U.freeVarSet ∪ V.freeVarSet) ∩ P_U.boundVarSet).toList TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.C_18_3	[889, 1]	[913, 13]	simp	case a U V P_U P_V : Formula h1 : IsReplOfFormulaInFormula U V P_U P_V h2 : IsProof (U.iff_ V) v : VarName a1 : (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v P_U ⊢ v ∈ ((U.freeVarSet ∪ V.freeVarSet) ∩ P_U.boundVarSet).toList	case a U V P_U P_V : Formula h1 : IsReplOfFormulaInFormula U V P_U P_V h2 : IsProof (U.iff_ V) v : VarName a1 : (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v P_U ⊢ (v ∈ U.freeVarSet ∨ v ∈ V.freeVarSet) ∧ v ∈ P_U.boundVarSet	Please generate a tactic in lean4 to solve the state. STATE: case a U V P_U P_V : Formula h1 : IsReplOfFormulaInFormula U V P_U P_V h2 : IsProof (U.iff_ V) v : VarName a1 : (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v P_U ⊢ v ∈ ((U.freeVarSet ∪ V.freeVarSet) ∩ P_U.boundVarSet).toList TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.C_18_3	[889, 1]	[913, 13]	simp only [isFreeIn_iff_mem_freeVarSet] at a1	case a U V P_U P_V : Formula h1 : IsReplOfFormulaInFormula U V P_U P_V h2 : IsProof (U.iff_ V) v : VarName a1 : (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v P_U ⊢ (v ∈ U.freeVarSet ∨ v ∈ V.freeVarSet) ∧ v ∈ P_U.boundVarSet	case a U V P_U P_V : Formula h1 : IsReplOfFormulaInFormula U V P_U P_V h2 : IsProof (U.iff_ V) v : VarName a1 : (v ∈ U.freeVarSet ∨ v ∈ V.freeVarSet) ∧ isBoundIn v P_U ⊢ (v ∈ U.freeVarSet ∨ v ∈ V.freeVarSet) ∧ v ∈ P_U.boundVarSet	Please generate a tactic in lean4 to solve the state. STATE: case a U V P_U P_V : Formula h1 : IsReplOfFormulaInFormula U V P_U P_V h2 : IsProof (U.iff_ V) v : VarName a1 : (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v P_U ⊢ (v ∈ U.freeVarSet ∨ v ∈ V.freeVarSet) ∧ v ∈ P_U.boundVarSet TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.C_18_3	[889, 1]	[913, 13]	simp only [isBoundIn_iff_mem_boundVarSet] at a1	case a U V P_U P_V : Formula h1 : IsReplOfFormulaInFormula U V P_U P_V h2 : IsProof (U.iff_ V) v : VarName a1 : (v ∈ U.freeVarSet ∨ v ∈ V.freeVarSet) ∧ isBoundIn v P_U ⊢ (v ∈ U.freeVarSet ∨ v ∈ V.freeVarSet) ∧ v ∈ P_U.boundVarSet	case a U V P_U P_V : Formula h1 : IsReplOfFormulaInFormula U V P_U P_V h2 : IsProof (U.iff_ V) v : VarName a1 : (v ∈ U.freeVarSet ∨ v ∈ V.freeVarSet) ∧ v ∈ P_U.boundVarSet ⊢ (v ∈ U.freeVarSet ∨ v ∈ V.freeVarSet) ∧ v ∈ P_U.boundVarSet	Please generate a tactic in lean4 to solve the state. STATE: case a U V P_U P_V : Formula h1 : IsReplOfFormulaInFormula U V P_U P_V h2 : IsProof (U.iff_ V) v : VarName a1 : (v ∈ U.freeVarSet ∨ v ∈ V.freeVarSet) ∧ isBoundIn v P_U ⊢ (v ∈ U.freeVarSet ∨ v ∈ V.freeVarSet) ∧ v ∈ P_U.boundVarSet TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.C_18_3	[889, 1]	[913, 13]	exact a1	case a U V P_U P_V : Formula h1 : IsReplOfFormulaInFormula U V P_U P_V h2 : IsProof (U.iff_ V) v : VarName a1 : (v ∈ U.freeVarSet ∨ v ∈ V.freeVarSet) ∧ v ∈ P_U.boundVarSet ⊢ (v ∈ U.freeVarSet ∨ v ∈ V.freeVarSet) ∧ v ∈ P_U.boundVarSet	no goals	Please generate a tactic in lean4 to solve the state. STATE: case a U V P_U P_V : Formula h1 : IsReplOfFormulaInFormula U V P_U P_V h2 : IsProof (U.iff_ V) v : VarName a1 : (v ∈ U.freeVarSet ∨ v ∈ V.freeVarSet) ∧ v ∈ P_U.boundVarSet ⊢ (v ∈ U.freeVarSet ∨ v ∈ V.freeVarSet) ∧ v ∈ P_U.boundVarSet TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.C_18_3	[889, 1]	[913, 13]	simp only [Formula.Forall_]	case a U V P_U P_V : Formula h1 : IsReplOfFormulaInFormula U V P_U P_V h2 : IsProof (U.iff_ V) ⊢ IsDeduct ∅ (Forall_ ((U.freeVarSet ∪ V.freeVarSet) ∩ P_U.boundVarSet).toList (U.iff_ V))	case a U V P_U P_V : Formula h1 : IsReplOfFormulaInFormula U V P_U P_V h2 : IsProof (U.iff_ V) ⊢ IsDeduct ∅ (List.foldr forall_ (U.iff_ V) ((U.freeVarSet ∪ V.freeVarSet) ∩ P_U.boundVarSet).toList)	Please generate a tactic in lean4 to solve the state. STATE: case a U V P_U P_V : Formula h1 : IsReplOfFormulaInFormula U V P_U P_V h2 : IsProof (U.iff_ V) ⊢ IsDeduct ∅ (Forall_ ((U.freeVarSet ∪ V.freeVarSet) ∩ P_U.boundVarSet).toList (U.iff_ V)) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.C_18_3	[889, 1]	[913, 13]	induction ((U.freeVarSet ∪ V.freeVarSet) ∩ P_U.boundVarSet).toList	case a U V P_U P_V : Formula h1 : IsReplOfFormulaInFormula U V P_U P_V h2 : IsProof (U.iff_ V) ⊢ IsDeduct ∅ (List.foldr forall_ (U.iff_ V) ((U.freeVarSet ∪ V.freeVarSet) ∩ P_U.boundVarSet).toList)	case a.nil U V P_U P_V : Formula h1 : IsReplOfFormulaInFormula U V P_U P_V h2 : IsProof (U.iff_ V) ⊢ IsDeduct ∅ (List.foldr forall_ (U.iff_ V) []) case a.cons U V P_U P_V : Formula h1 : IsReplOfFormulaInFormula U V P_U P_V h2 : IsProof (U.iff_ V) head✝ : VarName tail✝ : List VarName tail_ih✝ : IsDeduct ∅ (List.foldr f...	Please generate a tactic in lean4 to solve the state. STATE: case a U V P_U P_V : Formula h1 : IsReplOfFormulaInFormula U V P_U P_V h2 : IsProof (U.iff_ V) ⊢ IsDeduct ∅ (List.foldr forall_ (U.iff_ V) ((U.freeVarSet ∪ V.freeVarSet) ∩ P_U.boundVarSet).toList) TACTIC:
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/NV/Margaris/Fol.lean	FOL.NV.C_18_3	[889, 1]	[913, 13]	case _ => simp exact h2	U V P_U P_V : Formula h1 : IsReplOfFormulaInFormula U V P_U P_V h2 : IsProof (U.iff_ V) ⊢ IsDeduct ∅ (List.foldr forall_ (U.iff_ V) [])	no goals	Please generate a tactic in lean4 to solve the state. STATE: U V P_U P_V : Formula h1 : IsReplOfFormulaInFormula U V P_U P_V h2 : IsProof (U.iff_ V) ⊢ IsDeduct ∅ (List.foldr forall_ (U.iff_ V) []) TACTIC:

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