40 lines
1,010 B
Text
40 lines
1,010 B
Text
open nat
|
||
|
||
inductive vector (A : Type) : nat → Type :=
|
||
| nil {} : vector A zero
|
||
| cons : Π {n}, A → vector A n → vector A (succ n)
|
||
|
||
open vector
|
||
notation a :: b := cons a b
|
||
notation `[` l:(foldr `,` (h t, cons h t) nil `]`) := l
|
||
|
||
|
||
example (a b : nat) : succ a = succ b → a + 2 = b + 2 :=
|
||
begin
|
||
intro H,
|
||
injection H,
|
||
rewrite e_1
|
||
end
|
||
|
||
example (A : Type) (n : nat) (v w : vector A n) (a : A) (b : A) :
|
||
a :: v = b :: w → b = a :=
|
||
begin
|
||
intro H, injection H with neqn aeqb beqw,
|
||
rewrite aeqb
|
||
end
|
||
|
||
open prod
|
||
|
||
example (A : Type) (a₁ a₂ a₃ b₁ b₂ b₃ : A) : (a₁, a₂, a₃) = (b₁, b₂, b₃) → b₁ = a₁ :=
|
||
begin
|
||
intro H, injection H with a₁b₁ a₂b₂ a₃b₃,
|
||
rewrite a₁b₁
|
||
end
|
||
|
||
example (a₁ a₂ a₃ b₁ b₂ b₃ : nat) : (a₁+2, a₂+3, a₃+1) = (b₁+2, b₂+2, b₃+2) → b₁ = a₁ × a₃ = b₃+1 :=
|
||
begin
|
||
intro H, injection H with a₁b₁ sa₂b₂ a₃sb₃,
|
||
esimp at *,
|
||
rewrite [a₁b₁, a₃sb₃], split,
|
||
repeat trivial
|
||
end
|