24 lines
973 B
Text
24 lines
973 B
Text
set_option pp.notation false
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constant A : Type
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constants a b : A
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constant P : A → Type
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constant H₁ : a = a
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constant H₂ : P a
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constant H₃ : a = b
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constant f {A : Type} (a : A) : a = a
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#reduce (eq.rec H₂ (@f A a) : P a)
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#reduce (eq.rec H₂ H₁ : P a)
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#reduce (eq.rec H₂ H₃ : P b)
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#reduce (eq.rec H₂ (@eq.refl A a) : P a)
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-- eval λ (A : Type) (a b : A) (H₁ : a = a) (P : A → Prop) (H₂ : P a) (H₃ : a = a) (c : A), eq.rec (eq.rec H₂ H₁) H₃
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#check @eq.rec A a P H₂ a
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#check λ H : a = a, H₂
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inductive to_type {B : Type} : B → Type
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| mk : Π (b : B), to_type b
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noncomputable definition tst1 : to_type (λ H : a = a, H₂) := to_type.mk (@eq.rec A a P H₂ a)
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#check to_type.mk(λ H : a = a, H₂)
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#check to_type.mk(@eq.rec A a P H₂ a)
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#check to_type.mk(λ H : a = a, H₂) = to_type.mk(@eq.rec A a P H₂ a)
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-- #check to_type.mk(eq.rec H₂ H₁) = to_type.mk(H₂)
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-- #check to_type.mk(eq.rec H₂ (f a)) = to_type.mk(H₂)
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