f0f9880ece
new design for elim_match I still need to fix lemma generation, and refactor induction/subst tactics
31 lines
704 B
Text
31 lines
704 B
Text
set_option new_elaborator true
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inductive imf {A B : Type} (f : A → B) : B → Type
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| mk : ∀ (a : A), imf (f a)
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definition g {A B : Type} {f : A → B} : ∀ {b : B}, imf f b → A
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| .(f a) (imf.mk .f a) := a
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example {A B : Type} (f : A → B) (a : A) : g (imf.mk f a) = a :=
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rfl
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definition v₁ : imf nat.succ 1 :=
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(imf.mk nat.succ 0)
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definition v₂ : imf (λ x, 1 + x) 1 :=
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(imf.mk (λ x, 1 + x) 0)
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example : g v₁ = 0 :=
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rfl
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example : g v₂ = 0 :=
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rfl
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lemma ex1 (A : Type) : ∀ (a b : A) (H : a = b), b = a
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| a .a rfl := rfl
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lemma ex2 (A : Type) : ∀ a b : A, a = b → b = a
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| a .a (eq.refl .a) := rfl
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lemma ex3 (A : Type) : ∀ a b : A, a = b → b = a
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| a ._ (eq.refl ._) := rfl
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