Datasets:
internlm
/
Lean-Github

Dataset card Data Studio Files Community
1
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stringclasses
147 values
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https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/List.lean
List.nodup_eq_len_imp_exists_bijon
[162, 1]
[256, 30]
case inr c3 => obtain s1 := List.mem_map_of_mem f c3 simp only [a1_right] at s1 simp only [← a2] at s1 contradiction
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α x1_mem : x1 = xs_hd ∨ x1 ∈ xs_tl c1 : x1 = xs_hd c2 : ¬x2 = xs_hd a2 : ys_hd = f x2 c3 : x2 ∈ xs_tl ⊢ x1 = x2
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/List.lean
List.nodup_eq_len_imp_exists_bijon
[162, 1]
[256, 30]
contradiction
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α x1_mem : x1 = xs_hd ∨ x1 ∈ xs_tl c1 : x1 = xs_hd c2 : ¬x2 = xs_hd a2 : ys_hd = f x2 c3 : x2 = xs_hd ⊢ x1 = x2
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/List.lean
List.nodup_eq_len_imp_exists_bijon
[162, 1]
[256, 30]
obtain s1 := List.mem_map_of_mem f c3
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α x1_mem : x1 = xs_hd ∨ x1 ∈ xs_tl c1 : x1 = xs_hd c2 : ¬x2 = xs_hd a2 : ys_hd = f x2 c3 : x2 ∈ xs_tl ⊢ x1 = x2
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α x1_mem : x1 = xs_hd ∨ x1 ∈ xs_tl c1 : x1 = xs_hd c2 : ¬x2 = xs_hd a2 : ys_hd = f x2 c3 : x2 ∈ xs_tl s1 : f x2 ∈ map f xs_tl ⊢ x1 = x2
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/List.lean
List.nodup_eq_len_imp_exists_bijon
[162, 1]
[256, 30]
simp only [a1_right] at s1
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α x1_mem : x1 = xs_hd ∨ x1 ∈ xs_tl c1 : x1 = xs_hd c2 : ¬x2 = xs_hd a2 : ys_hd = f x2 c3 : x2 ∈ xs_tl s1 : f x2 ∈ map f xs_tl ⊢ x1 = x2
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α x1_mem : x1 = xs_hd ∨ x1 ∈ xs_tl c1 : x1 = xs_hd c2 : ¬x2 = xs_hd a2 : ys_hd = f x2 c3 : x2 ∈ xs_tl s1 : f x2 ∈ ys_tl ⊢ x1 = x2
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/List.lean
List.nodup_eq_len_imp_exists_bijon
[162, 1]
[256, 30]
simp only [← a2] at s1
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α x1_mem : x1 = xs_hd ∨ x1 ∈ xs_tl c1 : x1 = xs_hd c2 : ¬x2 = xs_hd a2 : ys_hd = f x2 c3 : x2 ∈ xs_tl s1 : f x2 ∈ ys_tl ⊢ x1 = x2
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α x1_mem : x1 = xs_hd ∨ x1 ∈ xs_tl c1 : x1 = xs_hd c2 : ¬x2 = xs_hd a2 : ys_hd = f x2 c3 : x2 ∈ xs_tl s1 : ys_hd ∈ ys_tl ⊢ x1 = x2
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/List.lean
List.nodup_eq_len_imp_exists_bijon
[162, 1]
[256, 30]
contradiction
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α x1_mem : x1 = xs_hd ∨ x1 ∈ xs_tl c1 : x1 = xs_hd c2 : ¬x2 = xs_hd a2 : ys_hd = f x2 c3 : x2 ∈ xs_tl s1 : ys_hd ∈ ys_tl ⊢ x1 = x2
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/List.lean
List.nodup_eq_len_imp_exists_bijon
[162, 1]
[256, 30]
intro a2
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α x1_mem : x1 = xs_hd ∨ x1 ∈ xs_tl x2_mem : x2 = xs_hd ∨ x2 ∈ xs_tl c1 : ¬x1 = xs_hd c2 : x2 = xs_hd ⊢ f x1 = ys_hd → x1 = x2
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α x1_mem : x1 = xs_hd ∨ x1 ∈ xs_tl x2_mem : x2 = xs_hd ∨ x2 ∈ xs_tl c1 : ¬x1 = xs_hd c2 : x2 = xs_hd a2 : f x1 = ys_hd ⊢ x1 = x2
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/List.lean
List.nodup_eq_len_imp_exists_bijon
[162, 1]
[256, 30]
cases x1_mem
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α x1_mem : x1 = xs_hd ∨ x1 ∈ xs_tl x2_mem : x2 = xs_hd ∨ x2 ∈ xs_tl c1 : ¬x1 = xs_hd c2 : x2 = xs_hd a2 : f x1 = ys_hd ⊢ x1 = x2
case inl α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α x2_mem : x2 = xs_hd ∨ x2 ∈ xs_tl c1 : ¬x1 = xs_hd c2 : x2 = xs_hd a2 : f x1 = ys_hd h✝ : x1 = xs_hd ⊢ x1 = x2 case inr α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α x2_mem : x2 = xs_hd ∨ x2 ∈ xs_tl c1 : ¬x1 = xs_hd c2 : x2 = xs_hd a2 : f x1 = ys_hd h✝ : x1 ∈ xs_tl ⊢ x1 = x2
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/List.lean
List.nodup_eq_len_imp_exists_bijon
[162, 1]
[256, 30]
case inl c3 => contradiction
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α x2_mem : x2 = xs_hd ∨ x2 ∈ xs_tl c1 : ¬x1 = xs_hd c2 : x2 = xs_hd a2 : f x1 = ys_hd c3 : x1 = xs_hd ⊢ x1 = x2
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/List.lean
List.nodup_eq_len_imp_exists_bijon
[162, 1]
[256, 30]
case inr c3 => obtain s1 := List.mem_map_of_mem f c3 simp only [a1_right] at s1 simp only [a2] at s1 contradiction
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α x2_mem : x2 = xs_hd ∨ x2 ∈ xs_tl c1 : ¬x1 = xs_hd c2 : x2 = xs_hd a2 : f x1 = ys_hd c3 : x1 ∈ xs_tl ⊢ x1 = x2
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/List.lean
List.nodup_eq_len_imp_exists_bijon
[162, 1]
[256, 30]
contradiction
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α x2_mem : x2 = xs_hd ∨ x2 ∈ xs_tl c1 : ¬x1 = xs_hd c2 : x2 = xs_hd a2 : f x1 = ys_hd c3 : x1 = xs_hd ⊢ x1 = x2
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/List.lean
List.nodup_eq_len_imp_exists_bijon
[162, 1]
[256, 30]
obtain s1 := List.mem_map_of_mem f c3
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α x2_mem : x2 = xs_hd ∨ x2 ∈ xs_tl c1 : ¬x1 = xs_hd c2 : x2 = xs_hd a2 : f x1 = ys_hd c3 : x1 ∈ xs_tl ⊢ x1 = x2
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α x2_mem : x2 = xs_hd ∨ x2 ∈ xs_tl c1 : ¬x1 = xs_hd c2 : x2 = xs_hd a2 : f x1 = ys_hd c3 : x1 ∈ xs_tl s1 : f x1 ∈ map f xs_tl ⊢ x1 = x2
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/List.lean
List.nodup_eq_len_imp_exists_bijon
[162, 1]
[256, 30]
simp only [a1_right] at s1
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α x2_mem : x2 = xs_hd ∨ x2 ∈ xs_tl c1 : ¬x1 = xs_hd c2 : x2 = xs_hd a2 : f x1 = ys_hd c3 : x1 ∈ xs_tl s1 : f x1 ∈ map f xs_tl ⊢ x1 = x2
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α x2_mem : x2 = xs_hd ∨ x2 ∈ xs_tl c1 : ¬x1 = xs_hd c2 : x2 = xs_hd a2 : f x1 = ys_hd c3 : x1 ∈ xs_tl s1 : f x1 ∈ ys_tl ⊢ x1 = x2
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/List.lean
List.nodup_eq_len_imp_exists_bijon
[162, 1]
[256, 30]
simp only [a2] at s1
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α x2_mem : x2 = xs_hd ∨ x2 ∈ xs_tl c1 : ¬x1 = xs_hd c2 : x2 = xs_hd a2 : f x1 = ys_hd c3 : x1 ∈ xs_tl s1 : f x1 ∈ ys_tl ⊢ x1 = x2
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α x2_mem : x2 = xs_hd ∨ x2 ∈ xs_tl c1 : ¬x1 = xs_hd c2 : x2 = xs_hd a2 : f x1 = ys_hd c3 : x1 ∈ xs_tl s1 : ys_hd ∈ ys_tl ⊢ x1 = x2
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/List.lean
List.nodup_eq_len_imp_exists_bijon
[162, 1]
[256, 30]
contradiction
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α x2_mem : x2 = xs_hd ∨ x2 ∈ xs_tl c1 : ¬x1 = xs_hd c2 : x2 = xs_hd a2 : f x1 = ys_hd c3 : x1 ∈ xs_tl s1 : ys_hd ∈ ys_tl ⊢ x1 = x2
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/List.lean
List.nodup_eq_len_imp_exists_bijon
[162, 1]
[256, 30]
intro a2
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α x1_mem : x1 = xs_hd ∨ x1 ∈ xs_tl x2_mem : x2 = xs_hd ∨ x2 ∈ xs_tl c1 : ¬x1 = xs_hd c2 : ¬x2 = xs_hd ⊢ f x1 = f x2 → x1 = x2
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α x1_mem : x1 = xs_hd ∨ x1 ∈ xs_tl x2_mem : x2 = xs_hd ∨ x2 ∈ xs_tl c1 : ¬x1 = xs_hd c2 : ¬x2 = xs_hd a2 : f x1 = f x2 ⊢ x1 = x2
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/List.lean
List.nodup_eq_len_imp_exists_bijon
[162, 1]
[256, 30]
cases x1_mem
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α x1_mem : x1 = xs_hd ∨ x1 ∈ xs_tl x2_mem : x2 = xs_hd ∨ x2 ∈ xs_tl c1 : ¬x1 = xs_hd c2 : ¬x2 = xs_hd a2 : f x1 = f x2 ⊢ x1 = x2
case inl α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α x2_mem : x2 = xs_hd ∨ x2 ∈ xs_tl c1 : ¬x1 = xs_hd c2 : ¬x2 = xs_hd a2 : f x1 = f x2 h✝ : x1 = xs_hd ⊢ x1 = x2 case inr α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α x2_mem : x2 = xs_hd ∨ x2 ∈ xs_tl c1 : ¬x1 = xs_hd c2 : ¬x2 = xs_hd a2 : f x1 = f x2 h✝ : x1 ∈ xs_tl ⊢ x1 = x2
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/List.lean
List.nodup_eq_len_imp_exists_bijon
[162, 1]
[256, 30]
case inl x1_mem_left => contradiction
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α x2_mem : x2 = xs_hd ∨ x2 ∈ xs_tl c1 : ¬x1 = xs_hd c2 : ¬x2 = xs_hd a2 : f x1 = f x2 x1_mem_left : x1 = xs_hd ⊢ x1 = x2
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/List.lean
List.nodup_eq_len_imp_exists_bijon
[162, 1]
[256, 30]
case inr x1_mem_right => cases x2_mem case inl x2_mem_left => contradiction case inr x2_mem_right => simp only [List.InjOn] at a1_left apply a1_left x1_mem_right x2_mem_right a2
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α x2_mem : x2 = xs_hd ∨ x2 ∈ xs_tl c1 : ¬x1 = xs_hd c2 : ¬x2 = xs_hd a2 : f x1 = f x2 x1_mem_right : x1 ∈ xs_tl ⊢ x1 = x2
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/List.lean
List.nodup_eq_len_imp_exists_bijon
[162, 1]
[256, 30]
contradiction
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α x2_mem : x2 = xs_hd ∨ x2 ∈ xs_tl c1 : ¬x1 = xs_hd c2 : ¬x2 = xs_hd a2 : f x1 = f x2 x1_mem_left : x1 = xs_hd ⊢ x1 = x2
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/List.lean
List.nodup_eq_len_imp_exists_bijon
[162, 1]
[256, 30]
cases x2_mem
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α x2_mem : x2 = xs_hd ∨ x2 ∈ xs_tl c1 : ¬x1 = xs_hd c2 : ¬x2 = xs_hd a2 : f x1 = f x2 x1_mem_right : x1 ∈ xs_tl ⊢ x1 = x2
case inl α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α c1 : ¬x1 = xs_hd c2 : ¬x2 = xs_hd a2 : f x1 = f x2 x1_mem_right : x1 ∈ xs_tl h✝ : x2 = xs_hd ⊢ x1 = x2 case inr α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α c1 : ¬x1 = xs_hd c2 : ¬x2 = xs_hd a2 : f x1 = f x2 x1_mem_right : x1 ∈ xs_tl h✝ : x2 ∈ xs_tl ⊢ x1 = x2
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/List.lean
List.nodup_eq_len_imp_exists_bijon
[162, 1]
[256, 30]
case inl x2_mem_left => contradiction
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α c1 : ¬x1 = xs_hd c2 : ¬x2 = xs_hd a2 : f x1 = f x2 x1_mem_right : x1 ∈ xs_tl x2_mem_left : x2 = xs_hd ⊢ x1 = x2
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/List.lean
List.nodup_eq_len_imp_exists_bijon
[162, 1]
[256, 30]
case inr x2_mem_right => simp only [List.InjOn] at a1_left apply a1_left x1_mem_right x2_mem_right a2
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α c1 : ¬x1 = xs_hd c2 : ¬x2 = xs_hd a2 : f x1 = f x2 x1_mem_right : x1 ∈ xs_tl x2_mem_right : x2 ∈ xs_tl ⊢ x1 = x2
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/List.lean
List.nodup_eq_len_imp_exists_bijon
[162, 1]
[256, 30]
contradiction
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α c1 : ¬x1 = xs_hd c2 : ¬x2 = xs_hd a2 : f x1 = f x2 x1_mem_right : x1 ∈ xs_tl x2_mem_left : x2 = xs_hd ⊢ x1 = x2
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/List.lean
List.nodup_eq_len_imp_exists_bijon
[162, 1]
[256, 30]
simp only [List.InjOn] at a1_left
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl x1 x2 : α c1 : ¬x1 = xs_hd c2 : ¬x2 = xs_hd a2 : f x1 = f x2 x1_mem_right : x1 ∈ xs_tl x2_mem_right : x2 ∈ xs_tl ⊢ x1 = x2
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : ∀ ⦃x₁ : α⦄, x₁ ∈ xs_tl → ∀ ⦃x₂ : α⦄, x₂ ∈ xs_tl → f x₁ = f x₂ → x₁ = x₂ a1_right : map f xs_tl = ys_tl x1 x2 : α c1 : ¬x1 = xs_hd c2 : ¬x2 = xs_hd a2 : f x1 = f x2 x1_mem_right : x1 ∈ xs_tl x2_mem_right : x2 ∈ xs_tl ⊢ x1 = x2
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/List.lean
List.nodup_eq_len_imp_exists_bijon
[162, 1]
[256, 30]
apply a1_left x1_mem_right x2_mem_right a2
α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : ∀ ⦃x₁ : α⦄, x₁ ∈ xs_tl → ∀ ⦃x₂ : α⦄, x₂ ∈ xs_tl → f x₁ = f x₂ → x₁ = x₂ a1_right : map f xs_tl = ys_tl x1 x2 : α c1 : ¬x1 = xs_hd c2 : ¬x2 = xs_hd a2 : f x1 = f x2 x1_mem_right : x1 ∈ xs_tl x2_mem_right : x2 ∈ xs_tl ⊢ x1 = x2
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/List.lean
List.nodup_eq_len_imp_exists_bijon
[162, 1]
[256, 30]
constructor
case right α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl ⊢ Function.updateITE f xs_hd ys_hd xs_hd = ys_hd ∧ map (Function.updateITE f xs_hd ys_hd) xs_tl = ys_tl
case right.left α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl ⊢ Function.updateITE f xs_hd ys_hd xs_hd = ys_hd case right.right α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl ⊢ map (Function.updateITE f xs_hd ys_hd) xs_tl = ys_tl
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/List.lean
List.nodup_eq_len_imp_exists_bijon
[162, 1]
[256, 30]
simp only [Function.updateITE]
case right.left α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl ⊢ Function.updateITE f xs_hd ys_hd xs_hd = ys_hd
case right.left α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl ⊢ (if True then ys_hd else f xs_hd) = ys_hd
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/List.lean
List.nodup_eq_len_imp_exists_bijon
[162, 1]
[256, 30]
simp
case right.left α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl ⊢ (if True then ys_hd else f xs_hd) = ys_hd
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/List.lean
List.nodup_eq_len_imp_exists_bijon
[162, 1]
[256, 30]
simp only [← a1_right]
case right.right α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl ⊢ map (Function.updateITE f xs_hd ys_hd) xs_tl = ys_tl
case right.right α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl ⊢ map (Function.updateITE f xs_hd ys_hd) xs_tl = map f xs_tl
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/List.lean
List.nodup_eq_len_imp_exists_bijon
[162, 1]
[256, 30]
apply Function.updateITE_not_mem_list
case right.right α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl ⊢ map (Function.updateITE f xs_hd ys_hd) xs_tl = map f xs_tl
case right.right.h1 α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl ⊢ xs_hd ∉ xs_tl
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/List.lean
List.nodup_eq_len_imp_exists_bijon
[162, 1]
[256, 30]
exact h2_left
case right.right.h1 α : Type inst✝ : DecidableEq α xs_hd : α xs_tl : List α ys_hd : α ys_tl : List α h1 : xs_tl.length = ys_tl.length h2_left : xs_hd ∉ xs_tl h2_right : xs_tl.Nodup h3_left : ys_hd ∉ ys_tl h3_right : ys_tl.Nodup f : α → α a1_left : InjOn f xs_tl a1_right : map f xs_tl = ys_tl ⊢ xs_hd ∉ xs_tl
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/List.lean
nodup_eq_len_imp_eqv
[259, 1]
[267, 11]
sorry
α : Type inst✝ : DecidableEq α xs ys : List α h1 : xs.length = ys.length h2 : xs.Nodup h3 : ys.Nodup ⊢ ∃ f, List.map (⇑f) xs = ys
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Except.lean
Except.bind_eq_ok
[7, 1]
[22, 9]
cases x
ε α β : Type x : Except ε α f : α → Except ε β a : β ⊢ x.bind f = ok a ↔ ∃ b, x = ok b ∧ f b = ok a
case error ε α β : Type f : α → Except ε β a : β a✝ : ε ⊢ (error a✝).bind f = ok a ↔ ∃ b, error a✝ = ok b ∧ f b = ok a case ok ε α β : Type f : α → Except ε β a : β a✝ : α ⊢ (ok a✝).bind f = ok a ↔ ∃ b, ok a✝ = ok b ∧ f b = ok a
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Except.lean
Except.bind_eq_ok
[7, 1]
[22, 9]
case error x => simp only [Except.bind] simp
ε α β : Type f : α → Except ε β a : β x : ε ⊢ (error x).bind f = ok a ↔ ∃ b, error x = ok b ∧ f b = ok a
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Except.lean
Except.bind_eq_ok
[7, 1]
[22, 9]
case ok x => simp only [Except.bind] simp
ε α β : Type f : α → Except ε β a : β x : α ⊢ (ok x).bind f = ok a ↔ ∃ b, ok x = ok b ∧ f b = ok a
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Except.lean
Except.bind_eq_ok
[7, 1]
[22, 9]
simp only [Except.bind]
ε α β : Type f : α → Except ε β a : β x : ε ⊢ (error x).bind f = ok a ↔ ∃ b, error x = ok b ∧ f b = ok a
ε α β : Type f : α → Except ε β a : β x : ε ⊢ False ↔ ∃ b, False ∧ f b = ok a
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Except.lean
Except.bind_eq_ok
[7, 1]
[22, 9]
simp
ε α β : Type f : α → Except ε β a : β x : ε ⊢ False ↔ ∃ b, False ∧ f b = ok a
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Except.lean
Except.bind_eq_ok
[7, 1]
[22, 9]
simp only [Except.bind]
ε α β : Type f : α → Except ε β a : β x : α ⊢ (ok x).bind f = ok a ↔ ∃ b, ok x = ok b ∧ f b = ok a
ε α β : Type f : α → Except ε β a : β x : α ⊢ f x = ok a ↔ ∃ b, ok x = ok b ∧ f b = ok a
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Except.lean
Except.bind_eq_ok
[7, 1]
[22, 9]
simp
ε α β : Type f : α → Except ε β a : β x : α ⊢ f x = ok a ↔ ∃ b, ok x = ok b ∧ f b = ok a
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Except.lean
Except.bind_eq_ok
[7, 1]
[22, 9]
cases x
ε α β : Type x : Except ε α f : α → Except ε β a : β ⊢ x.bind f = ok a ↔ ∃ b, x = ok b ∧ f b = ok a
case error ε α β : Type f : α → Except ε β a : β a✝ : ε ⊢ (error a✝).bind f = ok a ↔ ∃ b, error a✝ = ok b ∧ f b = ok a case ok ε α β : Type f : α → Except ε β a : β a✝ : α ⊢ (ok a✝).bind f = ok a ↔ ∃ b, ok a✝ = ok b ∧ f b = ok a
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Except.lean
Except.bind_eq_ok
[7, 1]
[22, 9]
case error x => simp only [Except.bind] simp
ε α β : Type f : α → Except ε β a : β x : ε ⊢ (error x).bind f = ok a ↔ ∃ b, error x = ok b ∧ f b = ok a
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Except.lean
Except.bind_eq_ok
[7, 1]
[22, 9]
case ok x => simp only [Except.bind] simp
ε α β : Type f : α → Except ε β a : β x : α ⊢ (ok x).bind f = ok a ↔ ∃ b, ok x = ok b ∧ f b = ok a
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Except.lean
Except.bind_eq_ok
[7, 1]
[22, 9]
simp only [Except.bind]
ε α β : Type f : α → Except ε β a : β x : ε ⊢ (error x).bind f = ok a ↔ ∃ b, error x = ok b ∧ f b = ok a
ε α β : Type f : α → Except ε β a : β x : ε ⊢ False ↔ ∃ b, False ∧ f b = ok a
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Except.lean
Except.bind_eq_ok
[7, 1]
[22, 9]
simp
ε α β : Type f : α → Except ε β a : β x : ε ⊢ False ↔ ∃ b, False ∧ f b = ok a
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Except.lean
Except.bind_eq_ok
[7, 1]
[22, 9]
simp only [Except.bind]
ε α β : Type f : α → Except ε β a : β x : α ⊢ (ok x).bind f = ok a ↔ ∃ b, ok x = ok b ∧ f b = ok a
ε α β : Type f : α → Except ε β a : β x : α ⊢ f x = ok a ↔ ∃ b, ok x = ok b ∧ f b = ok a
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Except.lean
Except.bind_eq_ok
[7, 1]
[22, 9]
simp
ε α β : Type f : α → Except ε β a : β x : α ⊢ f x = ok a ↔ ∃ b, ok x = ok b ∧ f b = ok a
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_1
[241, 1]
[253, 13]
apply IsDeduct.mp_ (forall_ v P)
P : Formula v t : VarName Δ : Set Formula h1 : IsDeduct Δ (forall_ v P) h2 : fastAdmits v t P ⊢ IsDeduct Δ (fastReplaceFree v t P)
case a P : Formula v t : VarName Δ : Set Formula h1 : IsDeduct Δ (forall_ v P) h2 : fastAdmits v t P ⊢ IsDeduct Δ ((forall_ v P).imp_ (fastReplaceFree v t P)) case a P : Formula v t : VarName Δ : Set Formula h1 : IsDeduct Δ (forall_ v P) h2 : fastAdmits v t P ⊢ IsDeduct Δ (forall_ v P)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_1
[241, 1]
[253, 13]
apply IsDeduct.axiom_
case a P : Formula v t : VarName Δ : Set Formula h1 : IsDeduct Δ (forall_ v P) h2 : fastAdmits v t P ⊢ IsDeduct Δ ((forall_ v P).imp_ (fastReplaceFree v t P))
case a.a P : Formula v t : VarName Δ : Set Formula h1 : IsDeduct Δ (forall_ v P) h2 : fastAdmits v t P ⊢ IsAxiom ((forall_ v P).imp_ (fastReplaceFree v t P))
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_1
[241, 1]
[253, 13]
apply IsAxiom.pred_2_ v t P (fastReplaceFree v t P) h2
case a.a P : Formula v t : VarName Δ : Set Formula h1 : IsDeduct Δ (forall_ v P) h2 : fastAdmits v t P ⊢ IsAxiom ((forall_ v P).imp_ (fastReplaceFree v t P))
case a.a P : Formula v t : VarName Δ : Set Formula h1 : IsDeduct Δ (forall_ v P) h2 : fastAdmits v t P ⊢ fastReplaceFree v t P = fastReplaceFree v t P
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_1
[241, 1]
[253, 13]
rfl
case a.a P : Formula v t : VarName Δ : Set Formula h1 : IsDeduct Δ (forall_ v P) h2 : fastAdmits v t P ⊢ fastReplaceFree v t P = fastReplaceFree v t P
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_1
[241, 1]
[253, 13]
exact h1
case a P : Formula v t : VarName Δ : Set Formula h1 : IsDeduct Δ (forall_ v P) h2 : fastAdmits v t P ⊢ IsDeduct Δ (forall_ v P)
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.specId
[259, 1]
[271, 13]
apply IsDeduct.mp_ (forall_ v P)
v : VarName P : Formula Δ : Set Formula h1 : IsDeduct Δ (forall_ v P) ⊢ IsDeduct Δ P
case a v : VarName P : Formula Δ : Set Formula h1 : IsDeduct Δ (forall_ v P) ⊢ IsDeduct Δ ((forall_ v P).imp_ P) case a v : VarName P : Formula Δ : Set Formula h1 : IsDeduct Δ (forall_ v P) ⊢ IsDeduct Δ (forall_ v P)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.specId
[259, 1]
[271, 13]
apply IsDeduct.axiom_
case a v : VarName P : Formula Δ : Set Formula h1 : IsDeduct Δ (forall_ v P) ⊢ IsDeduct Δ ((forall_ v P).imp_ P)
case a.a v : VarName P : Formula Δ : Set Formula h1 : IsDeduct Δ (forall_ v P) ⊢ IsAxiom ((forall_ v P).imp_ P)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.specId
[259, 1]
[271, 13]
apply IsAxiom.pred_2_ v v P
case a.a v : VarName P : Formula Δ : Set Formula h1 : IsDeduct Δ (forall_ v P) ⊢ IsAxiom ((forall_ v P).imp_ P)
case a.a.a v : VarName P : Formula Δ : Set Formula h1 : IsDeduct Δ (forall_ v P) ⊢ fastAdmits v v P case a.a.a v : VarName P : Formula Δ : Set Formula h1 : IsDeduct Δ (forall_ v P) ⊢ fastReplaceFree v v P = P
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.specId
[259, 1]
[271, 13]
exact fastAdmits_self P v
case a.a.a v : VarName P : Formula Δ : Set Formula h1 : IsDeduct Δ (forall_ v P) ⊢ fastAdmits v v P
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.specId
[259, 1]
[271, 13]
exact fastReplaceFree_self P v
case a.a.a v : VarName P : Formula Δ : Set Formula h1 : IsDeduct Δ (forall_ v P) ⊢ fastReplaceFree v v P = P
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.specId
[259, 1]
[271, 13]
exact h1
case a v : VarName P : Formula Δ : Set Formula h1 : IsDeduct Δ (forall_ v P) ⊢ IsDeduct Δ (forall_ v P)
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_3
[276, 1]
[295, 10]
simp only [fastAdmits] at h1
P : Formula v t : VarName h1 : fastAdmits v t P ⊢ IsProof ((fastReplaceFree v t P).imp_ (exists_ v P))
P : Formula v t : VarName h1 : fastAdmitsAux v t ∅ P ⊢ IsProof ((fastReplaceFree v t P).imp_ (exists_ v P))
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_3
[276, 1]
[295, 10]
simp only [def_exists_]
P : Formula v t : VarName h1 : fastAdmitsAux v t ∅ P ⊢ IsProof ((fastReplaceFree v t P).imp_ (exists_ v P))
P : Formula v t : VarName h1 : fastAdmitsAux v t ∅ P ⊢ IsProof ((fastReplaceFree v t P).imp_ (forall_ v P.not_).not_)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_3
[276, 1]
[295, 10]
simp only [IsProof]
P : Formula v t : VarName h1 : fastAdmitsAux v t ∅ P ⊢ IsProof ((fastReplaceFree v t P).imp_ (forall_ v P.not_).not_)
P : Formula v t : VarName h1 : fastAdmitsAux v t ∅ P ⊢ IsDeduct ∅ ((fastReplaceFree v t P).imp_ (forall_ v P.not_).not_)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_3
[276, 1]
[295, 10]
apply IsDeduct.mp_ ((forall_ v P.not_).imp_ (fastReplaceFree v t P).not_)
P : Formula v t : VarName h1 : fastAdmitsAux v t ∅ P ⊢ IsDeduct ∅ ((fastReplaceFree v t P).imp_ (forall_ v P.not_).not_)
case a P : Formula v t : VarName h1 : fastAdmitsAux v t ∅ P ⊢ IsDeduct ∅ (((forall_ v P.not_).imp_ (fastReplaceFree v t P).not_).imp_ ((fastReplaceFree v t P).imp_ (forall_ v P.not_).not_)) case a P : Formula v t : VarName h1 : fastAdmitsAux v t ∅ P ⊢ IsDeduct ∅ ((forall_ v P.not_).imp_ (fastReplaceFree v t P).not_)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_3
[276, 1]
[295, 10]
SC
case a P : Formula v t : VarName h1 : fastAdmitsAux v t ∅ P ⊢ IsDeduct ∅ (((forall_ v P.not_).imp_ (fastReplaceFree v t P).not_).imp_ ((fastReplaceFree v t P).imp_ (forall_ v P.not_).not_))
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_3
[276, 1]
[295, 10]
apply IsDeduct.axiom_
case a P : Formula v t : VarName h1 : fastAdmitsAux v t ∅ P ⊢ IsDeduct ∅ ((forall_ v P.not_).imp_ (fastReplaceFree v t P).not_)
case a.a P : Formula v t : VarName h1 : fastAdmitsAux v t ∅ P ⊢ IsAxiom ((forall_ v P.not_).imp_ (fastReplaceFree v t P).not_)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_3
[276, 1]
[295, 10]
apply IsAxiom.pred_2_ v t
case a.a P : Formula v t : VarName h1 : fastAdmitsAux v t ∅ P ⊢ IsAxiom ((forall_ v P.not_).imp_ (fastReplaceFree v t P).not_)
case a.a.a P : Formula v t : VarName h1 : fastAdmitsAux v t ∅ P ⊢ fastAdmits v t P.not_ case a.a.a P : Formula v t : VarName h1 : fastAdmitsAux v t ∅ P ⊢ fastReplaceFree v t P.not_ = (fastReplaceFree v t P).not_
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_3
[276, 1]
[295, 10]
simp only [fastAdmits]
case a.a.a P : Formula v t : VarName h1 : fastAdmitsAux v t ∅ P ⊢ fastAdmits v t P.not_
case a.a.a P : Formula v t : VarName h1 : fastAdmitsAux v t ∅ P ⊢ fastAdmitsAux v t ∅ P.not_
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_3
[276, 1]
[295, 10]
simp only [fastAdmitsAux]
case a.a.a P : Formula v t : VarName h1 : fastAdmitsAux v t ∅ P ⊢ fastAdmitsAux v t ∅ P.not_
case a.a.a P : Formula v t : VarName h1 : fastAdmitsAux v t ∅ P ⊢ fastAdmitsAux v t ∅ P
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_3
[276, 1]
[295, 10]
exact h1
case a.a.a P : Formula v t : VarName h1 : fastAdmitsAux v t ∅ P ⊢ fastAdmitsAux v t ∅ P
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_3
[276, 1]
[295, 10]
rfl
case a.a.a P : Formula v t : VarName h1 : fastAdmitsAux v t ∅ P ⊢ fastReplaceFree v t P.not_ = (fastReplaceFree v t P).not_
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_4
[299, 1]
[311, 13]
apply IsDeduct.mp_ (fastReplaceFree v t P)
P : Formula v t : VarName Δ : Set Formula h1 : fastAdmits v t P h2 : IsDeduct Δ (fastReplaceFree v t P) ⊢ IsDeduct Δ (exists_ v P)
case a P : Formula v t : VarName Δ : Set Formula h1 : fastAdmits v t P h2 : IsDeduct Δ (fastReplaceFree v t P) ⊢ IsDeduct Δ ((fastReplaceFree v t P).imp_ (exists_ v P)) case a P : Formula v t : VarName Δ : Set Formula h1 : fastAdmits v t P h2 : IsDeduct Δ (fastReplaceFree v t P) ⊢ IsDeduct Δ (fastReplaceFree v t P)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_4
[299, 1]
[311, 13]
apply proof_imp_deduct
case a P : Formula v t : VarName Δ : Set Formula h1 : fastAdmits v t P h2 : IsDeduct Δ (fastReplaceFree v t P) ⊢ IsDeduct Δ ((fastReplaceFree v t P).imp_ (exists_ v P))
case a.h1 P : Formula v t : VarName Δ : Set Formula h1 : fastAdmits v t P h2 : IsDeduct Δ (fastReplaceFree v t P) ⊢ IsProof ((fastReplaceFree v t P).imp_ (exists_ v P))
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_4
[299, 1]
[311, 13]
apply T_17_3
case a.h1 P : Formula v t : VarName Δ : Set Formula h1 : fastAdmits v t P h2 : IsDeduct Δ (fastReplaceFree v t P) ⊢ IsProof ((fastReplaceFree v t P).imp_ (exists_ v P))
case a.h1.h1 P : Formula v t : VarName Δ : Set Formula h1 : fastAdmits v t P h2 : IsDeduct Δ (fastReplaceFree v t P) ⊢ fastAdmits v t P
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_4
[299, 1]
[311, 13]
exact h1
case a.h1.h1 P : Formula v t : VarName Δ : Set Formula h1 : fastAdmits v t P h2 : IsDeduct Δ (fastReplaceFree v t P) ⊢ fastAdmits v t P
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_4
[299, 1]
[311, 13]
exact h2
case a P : Formula v t : VarName Δ : Set Formula h1 : fastAdmits v t P h2 : IsDeduct Δ (fastReplaceFree v t P) ⊢ IsDeduct Δ (fastReplaceFree v t P)
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.existsIntroId
[316, 1]
[326, 13]
apply T_17_4 P v v Δ
P : Formula v : VarName Δ : Set Formula h1 : IsDeduct Δ P ⊢ IsDeduct Δ (exists_ v P)
case h1 P : Formula v : VarName Δ : Set Formula h1 : IsDeduct Δ P ⊢ fastAdmits v v P case h2 P : Formula v : VarName Δ : Set Formula h1 : IsDeduct Δ P ⊢ IsDeduct Δ (fastReplaceFree v v P)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.existsIntroId
[316, 1]
[326, 13]
exact fastAdmits_self P v
case h1 P : Formula v : VarName Δ : Set Formula h1 : IsDeduct Δ P ⊢ fastAdmits v v P
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.existsIntroId
[316, 1]
[326, 13]
simp only [fastReplaceFree_self]
case h2 P : Formula v : VarName Δ : Set Formula h1 : IsDeduct Δ P ⊢ IsDeduct Δ (fastReplaceFree v v P)
case h2 P : Formula v : VarName Δ : Set Formula h1 : IsDeduct Δ P ⊢ IsDeduct Δ P
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.existsIntroId
[316, 1]
[326, 13]
exact h1
case h2 P : Formula v : VarName Δ : Set Formula h1 : IsDeduct Δ P ⊢ IsDeduct Δ P
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_6
[329, 1]
[339, 7]
apply deduction_theorem
P : Formula v : VarName ⊢ IsProof ((forall_ v P).imp_ (exists_ v P))
case h1 P : Formula v : VarName ⊢ IsDeduct (∅ ∪ {forall_ v P}) (exists_ v P)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_6
[329, 1]
[339, 7]
simp
case h1 P : Formula v : VarName ⊢ IsDeduct (∅ ∪ {forall_ v P}) (exists_ v P)
case h1 P : Formula v : VarName ⊢ IsDeduct {forall_ v P} (exists_ v P)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_6
[329, 1]
[339, 7]
apply existsIntroId
case h1 P : Formula v : VarName ⊢ IsDeduct {forall_ v P} (exists_ v P)
case h1.h1 P : Formula v : VarName ⊢ IsDeduct {forall_ v P} P
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_6
[329, 1]
[339, 7]
apply specId v
case h1.h1 P : Formula v : VarName ⊢ IsDeduct {forall_ v P} P
case h1.h1.h1 P : Formula v : VarName ⊢ IsDeduct {forall_ v P} (forall_ v P)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_6
[329, 1]
[339, 7]
apply IsDeduct.assume_
case h1.h1.h1 P : Formula v : VarName ⊢ IsDeduct {forall_ v P} (forall_ v P)
case h1.h1.h1.a P : Formula v : VarName ⊢ forall_ v P ∈ {forall_ v P}
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_6
[329, 1]
[339, 7]
simp
case h1.h1.h1.a P : Formula v : VarName ⊢ forall_ v P ∈ {forall_ v P}
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_7
[342, 1]
[368, 20]
induction h1
F : Formula v : VarName Δ : Set Formula h1 : IsDeduct Δ F h2 : ∀ H ∈ Δ, ¬isFreeIn v H ⊢ IsDeduct Δ (forall_ v F)
case axiom_ F : Formula v : VarName Δ : Set Formula h2 : ∀ H ∈ Δ, ¬isFreeIn v H phi✝ : Formula a✝ : IsAxiom phi✝ ⊢ IsDeduct Δ (forall_ v phi✝) case assume_ F : Formula v : VarName Δ : Set Formula h2 : ∀ H ∈ Δ, ¬isFreeIn v H phi✝ : Formula a✝ : phi✝ ∈ Δ ⊢ IsDeduct Δ (forall_ v phi✝) case mp_ F : Formula v : VarName Δ : Set Formula h2 : ∀ H ∈ Δ, ¬isFreeIn v H phi✝ psi✝ : Formula a✝¹ : IsDeduct Δ (phi✝.imp_ psi✝) a✝ : IsDeduct Δ phi✝ a_ih✝¹ : IsDeduct Δ (forall_ v (phi✝.imp_ psi✝)) a_ih✝ : IsDeduct Δ (forall_ v phi✝) ⊢ IsDeduct Δ (forall_ v psi✝)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_7
[342, 1]
[368, 20]
case axiom_ h1_phi h1_1 => apply IsDeduct.axiom_ apply IsAxiom.gen_ exact h1_1
F : Formula v : VarName Δ : Set Formula h2 : ∀ H ∈ Δ, ¬isFreeIn v H h1_phi : Formula h1_1 : IsAxiom h1_phi ⊢ IsDeduct Δ (forall_ v h1_phi)
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_7
[342, 1]
[368, 20]
apply IsDeduct.axiom_
F : Formula v : VarName Δ : Set Formula h2 : ∀ H ∈ Δ, ¬isFreeIn v H h1_phi : Formula h1_1 : IsAxiom h1_phi ⊢ IsDeduct Δ (forall_ v h1_phi)
case a F : Formula v : VarName Δ : Set Formula h2 : ∀ H ∈ Δ, ¬isFreeIn v H h1_phi : Formula h1_1 : IsAxiom h1_phi ⊢ IsAxiom (forall_ v h1_phi)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_7
[342, 1]
[368, 20]
apply IsAxiom.gen_
case a F : Formula v : VarName Δ : Set Formula h2 : ∀ H ∈ Δ, ¬isFreeIn v H h1_phi : Formula h1_1 : IsAxiom h1_phi ⊢ IsAxiom (forall_ v h1_phi)
case a.a F : Formula v : VarName Δ : Set Formula h2 : ∀ H ∈ Δ, ¬isFreeIn v H h1_phi : Formula h1_1 : IsAxiom h1_phi ⊢ IsAxiom h1_phi
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_7
[342, 1]
[368, 20]
exact h1_1
case a.a F : Formula v : VarName Δ : Set Formula h2 : ∀ H ∈ Δ, ¬isFreeIn v H h1_phi : Formula h1_1 : IsAxiom h1_phi ⊢ IsAxiom h1_phi
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_7
[342, 1]
[368, 20]
apply IsDeduct.mp_ h1_phi
F : Formula v : VarName Δ : Set Formula h2 : ∀ H ∈ Δ, ¬isFreeIn v H h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ IsDeduct Δ (forall_ v h1_phi)
case a F : Formula v : VarName Δ : Set Formula h2 : ∀ H ∈ Δ, ¬isFreeIn v H h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ IsDeduct Δ (h1_phi.imp_ (forall_ v h1_phi)) case a F : Formula v : VarName Δ : Set Formula h2 : ∀ H ∈ Δ, ¬isFreeIn v H h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ IsDeduct Δ h1_phi
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_7
[342, 1]
[368, 20]
apply IsDeduct.axiom_
case a F : Formula v : VarName Δ : Set Formula h2 : ∀ H ∈ Δ, ¬isFreeIn v H h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ IsDeduct Δ (h1_phi.imp_ (forall_ v h1_phi))
case a.a F : Formula v : VarName Δ : Set Formula h2 : ∀ H ∈ Δ, ¬isFreeIn v H h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ IsAxiom (h1_phi.imp_ (forall_ v h1_phi))
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_7
[342, 1]
[368, 20]
apply IsAxiom.pred_3_
case a.a F : Formula v : VarName Δ : Set Formula h2 : ∀ H ∈ Δ, ¬isFreeIn v H h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ IsAxiom (h1_phi.imp_ (forall_ v h1_phi))
case a.a.a F : Formula v : VarName Δ : Set Formula h2 : ∀ H ∈ Δ, ¬isFreeIn v H h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ ¬isFreeIn v h1_phi
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_7
[342, 1]
[368, 20]
exact h2 h1_phi h1_1
case a.a.a F : Formula v : VarName Δ : Set Formula h2 : ∀ H ∈ Δ, ¬isFreeIn v H h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ ¬isFreeIn v h1_phi
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_7
[342, 1]
[368, 20]
apply IsDeduct.assume_
case a F : Formula v : VarName Δ : Set Formula h2 : ∀ H ∈ Δ, ¬isFreeIn v H h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ IsDeduct Δ h1_phi
case a.a F : Formula v : VarName Δ : Set Formula h2 : ∀ H ∈ Δ, ¬isFreeIn v H h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ h1_phi ∈ Δ
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_7
[342, 1]
[368, 20]
exact h1_1
case a.a F : Formula v : VarName Δ : Set Formula h2 : ∀ H ∈ Δ, ¬isFreeIn v H h1_phi : Formula h1_1 : h1_phi ∈ Δ ⊢ h1_phi ∈ Δ
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_7
[342, 1]
[368, 20]
apply IsDeduct.mp_ (forall_ v h1_phi)
F : Formula v : VarName Δ : Set Formula h2 : ∀ H ∈ Δ, ¬isFreeIn v H h1_phi h1_psi : Formula a✝¹ : IsDeduct Δ (h1_phi.imp_ h1_psi) a✝ : IsDeduct Δ h1_phi h1_ih_1 : IsDeduct Δ (forall_ v (h1_phi.imp_ h1_psi)) h1_ih_2 : IsDeduct Δ (forall_ v h1_phi) ⊢ IsDeduct Δ (forall_ v h1_psi)
case a F : Formula v : VarName Δ : Set Formula h2 : ∀ H ∈ Δ, ¬isFreeIn v H h1_phi h1_psi : Formula a✝¹ : IsDeduct Δ (h1_phi.imp_ h1_psi) a✝ : IsDeduct Δ h1_phi h1_ih_1 : IsDeduct Δ (forall_ v (h1_phi.imp_ h1_psi)) h1_ih_2 : IsDeduct Δ (forall_ v h1_phi) ⊢ IsDeduct Δ ((forall_ v h1_phi).imp_ (forall_ v h1_psi)) case a F : Formula v : VarName Δ : Set Formula h2 : ∀ H ∈ Δ, ¬isFreeIn v H h1_phi h1_psi : Formula a✝¹ : IsDeduct Δ (h1_phi.imp_ h1_psi) a✝ : IsDeduct Δ h1_phi h1_ih_1 : IsDeduct Δ (forall_ v (h1_phi.imp_ h1_psi)) h1_ih_2 : IsDeduct Δ (forall_ v h1_phi) ⊢ IsDeduct Δ (forall_ v h1_phi)
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_7
[342, 1]
[368, 20]
apply IsDeduct.mp_ (forall_ v (h1_phi.imp_ h1_psi))
case a F : Formula v : VarName Δ : Set Formula h2 : ∀ H ∈ Δ, ¬isFreeIn v H h1_phi h1_psi : Formula a✝¹ : IsDeduct Δ (h1_phi.imp_ h1_psi) a✝ : IsDeduct Δ h1_phi h1_ih_1 : IsDeduct Δ (forall_ v (h1_phi.imp_ h1_psi)) h1_ih_2 : IsDeduct Δ (forall_ v h1_phi) ⊢ IsDeduct Δ ((forall_ v h1_phi).imp_ (forall_ v h1_psi))
case a.a F : Formula v : VarName Δ : Set Formula h2 : ∀ H ∈ Δ, ¬isFreeIn v H h1_phi h1_psi : Formula a✝¹ : IsDeduct Δ (h1_phi.imp_ h1_psi) a✝ : IsDeduct Δ h1_phi h1_ih_1 : IsDeduct Δ (forall_ v (h1_phi.imp_ h1_psi)) h1_ih_2 : IsDeduct Δ (forall_ v h1_phi) ⊢ IsDeduct Δ ((forall_ v (h1_phi.imp_ h1_psi)).imp_ ((forall_ v h1_phi).imp_ (forall_ v h1_psi))) case a.a F : Formula v : VarName Δ : Set Formula h2 : ∀ H ∈ Δ, ¬isFreeIn v H h1_phi h1_psi : Formula a✝¹ : IsDeduct Δ (h1_phi.imp_ h1_psi) a✝ : IsDeduct Δ h1_phi h1_ih_1 : IsDeduct Δ (forall_ v (h1_phi.imp_ h1_psi)) h1_ih_2 : IsDeduct Δ (forall_ v h1_phi) ⊢ IsDeduct Δ (forall_ v (h1_phi.imp_ h1_psi))
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_7
[342, 1]
[368, 20]
apply IsDeduct.axiom_
case a.a F : Formula v : VarName Δ : Set Formula h2 : ∀ H ∈ Δ, ¬isFreeIn v H h1_phi h1_psi : Formula a✝¹ : IsDeduct Δ (h1_phi.imp_ h1_psi) a✝ : IsDeduct Δ h1_phi h1_ih_1 : IsDeduct Δ (forall_ v (h1_phi.imp_ h1_psi)) h1_ih_2 : IsDeduct Δ (forall_ v h1_phi) ⊢ IsDeduct Δ ((forall_ v (h1_phi.imp_ h1_psi)).imp_ ((forall_ v h1_phi).imp_ (forall_ v h1_psi)))
case a.a.a F : Formula v : VarName Δ : Set Formula h2 : ∀ H ∈ Δ, ¬isFreeIn v H h1_phi h1_psi : Formula a✝¹ : IsDeduct Δ (h1_phi.imp_ h1_psi) a✝ : IsDeduct Δ h1_phi h1_ih_1 : IsDeduct Δ (forall_ v (h1_phi.imp_ h1_psi)) h1_ih_2 : IsDeduct Δ (forall_ v h1_phi) ⊢ IsAxiom ((forall_ v (h1_phi.imp_ h1_psi)).imp_ ((forall_ v h1_phi).imp_ (forall_ v h1_psi)))
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_7
[342, 1]
[368, 20]
apply IsAxiom.pred_1_
case a.a.a F : Formula v : VarName Δ : Set Formula h2 : ∀ H ∈ Δ, ¬isFreeIn v H h1_phi h1_psi : Formula a✝¹ : IsDeduct Δ (h1_phi.imp_ h1_psi) a✝ : IsDeduct Δ h1_phi h1_ih_1 : IsDeduct Δ (forall_ v (h1_phi.imp_ h1_psi)) h1_ih_2 : IsDeduct Δ (forall_ v h1_phi) ⊢ IsAxiom ((forall_ v (h1_phi.imp_ h1_psi)).imp_ ((forall_ v h1_phi).imp_ (forall_ v h1_psi)))
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Margaris/Fol.lean
FOL.NV.T_17_7
[342, 1]
[368, 20]
exact h1_ih_1
case a.a F : Formula v : VarName Δ : Set Formula h2 : ∀ H ∈ Δ, ¬isFreeIn v H h1_phi h1_psi : Formula a✝¹ : IsDeduct Δ (h1_phi.imp_ h1_psi) a✝ : IsDeduct Δ h1_phi h1_ih_1 : IsDeduct Δ (forall_ v (h1_phi.imp_ h1_psi)) h1_ih_2 : IsDeduct Δ (forall_ v h1_phi) ⊢ IsDeduct Δ (forall_ v (h1_phi.imp_ h1_psi))
no goals