39 lines
925 B
Text
39 lines
925 B
Text
|
import data.list
|
|||
|
|
open nat list
|
|||
|
|
|
|||
|
|
example (H : false) : (1 : ℕ) + 1 = (2 : ℕ) :=
|
|||
|
|
begin
|
|||
|
|
replace (1 : ℕ) with (succ 0) at {1},
|
|||
|
|
end
|
|||
|
|
|
|||
|
|
example (H : false) : (1 : ℕ) + 1 = (2 : ℕ) :=
|
|||
|
|
begin
|
|||
|
|
replace (1 : ℕ) with (succ 1),
|
|||
|
|
end
|
|||
|
|
|
|||
|
|
definition foo (n : ℕ) : ℕ := n
|
|||
|
|
definition bar := foo
|
|||
|
|
example (h : true) : foo 2 = bar 2 :=
|
|||
|
|
begin
|
|||
|
|
replace foo 2 with bar 2 at h,
|
|||
|
|
reflexivity
|
|||
|
|
end
|
|||
|
|
|
|||
|
|
constants (P : ℕ → Type₁) (p : P (3 + 1)) (f : Πn, P n)
|
|||
|
|
example : f (3 + 1) = p :=
|
|||
|
|
begin
|
|||
|
|
replace ((3 : ℕ) + 1) with (4 : ℕ),
|
|||
|
|
end
|
|||
|
|
|
|||
|
|
variables {A B : Type}
|
|||
|
|
lemma my_map_concat (f : A → B) (a : A) : Πl, map f (concat a l) = concat (f a) (map f l)
|
|||
|
|
| nil := rfl
|
|||
|
|
| (b::l) := begin
|
|||
|
|
replace concat a (b :: l) with b :: concat a l,
|
|||
|
|
replace concat (f a) (map f (b :: l)) with f b :: concat (f a) (map f l),
|
|||
|
|
replace map f (b :: concat a l) with f b :: map f (concat a l),
|
|||
|
|
congruence,
|
|||
|
|
apply my_map_concat
|
|||
|
|
|
|||
|
|
end
|