18 lines
586 B
Text
18 lines
586 B
Text
constant A₁ : Type
|
|
constant A₂ : A₁ → Type
|
|
constant A₃ : Π (a₁ : A₁), A₂ a₁ → Type
|
|
|
|
structure foo :=
|
|
mk :: (a₁ : A₁) (a₂ : A₂ a₁) (a₃ : A₃ a₁ a₂)
|
|
|
|
theorem foo.eq {a₁ b₁ : A₁} {a₂ : A₂ a₁} {b₂ : A₂ b₁} {a₃ : A₃ a₁ a₂} {b₃ : A₃ b₁ b₂}
|
|
(H₁ : a₁ = b₁) (H₂ : eq.rec_on H₁ a₂ = b₂) (H₃ : eq.rec_on H₂ (eq.rec_on H₁ a₃) = b₃)
|
|
: foo.mk a₁ a₂ a₃ = foo.mk b₁ b₂ b₃ :=
|
|
begin
|
|
cases H₁,
|
|
cases H₂,
|
|
cases H₃,
|
|
apply rfl
|
|
end
|
|
|
|
print definition foo.eq
|