26 lines
907 B
Text
26 lines
907 B
Text
|
import logic
|
||
|
|
set_option pp.notation false
|
||
|
|
constant A : Type
|
||
|
|
constants a b : A
|
||
|
|
constant P : A → Type
|
||
|
|
constant H₁ : a = a
|
||
|
|
constant H₂ : P a
|
||
|
|
constant H₃ : a = b
|
||
|
|
constant f {A : Type} (a : A) : a = a
|
||
|
|
eval eq.rec H₂ (f a)
|
||
|
|
eval eq.rec H₂ H₁
|
||
|
|
eval eq.rec H₂ H₃
|
||
|
|
eval eq.rec H₂ (eq.refl a)
|
||
|
|
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
|
||
|
|
check @eq.rec A a P H₂ a
|
||
|
|
check λ H : a = a, H₂
|
||
|
|
inductive to_type {B : Type} : B → Type :=
|
||
|
|
mk : Π (b : B), to_type b
|
||
|
|
|
||
|
|
definition tst1 : to_type (λ H : a = a, H₂) := to_type.mk (@eq.rec A a P H₂ a)
|
||
|
|
check to_type.mk(λ H : a = a, H₂)
|
||
|
|
check to_type.mk(@eq.rec A a P H₂ a)
|
||
|
|
check to_type.mk(λ H : a = a, H₂) = to_type.mk(@eq.rec A a P H₂ a)
|
||
|
|
check to_type.mk(eq.rec H₂ H₁) = to_type.mk(H₂)
|
||
|
|
check to_type.mk(eq.rec H₂ (f a)) = to_type.mk(H₂)
|