692701c5ef
The idea is to make sure lean doesn't timeout (at reflexivity) when we apply simp or
rewrite in goals such as
(x y : nat) |- x + y + 10000000000 = x + y + 200000000000000
This commit also addresses an issue raised at #1218
36 lines
950 B
Text
36 lines
950 B
Text
prelude
|
|
import init.meta init.logic init.data.nat.lemmas
|
|
import init.data.char.basic
|
|
|
|
namespace char
|
|
lemma of_nat_eq_of_lt {n : nat} : ∀ h : n < char_sz, of_nat n = fin.mk n h :=
|
|
begin
|
|
intro h,
|
|
unfold of_nat,
|
|
cases (nat.decidable_lt n char_sz),
|
|
{contradiction},
|
|
{reflexivity}
|
|
end
|
|
|
|
lemma of_nat_eq_fin_of_ge {n : nat} : n ≥ char_sz → of_nat n = fin.mk 0 zero_lt_char_sz :=
|
|
begin
|
|
intro h,
|
|
unfold of_nat,
|
|
cases (nat.decidable_lt n char_sz),
|
|
{reflexivity},
|
|
{note h' := not_lt_of_ge h, contradiction}
|
|
end
|
|
|
|
lemma of_nat_eq_of_ge {n : nat} : n ≥ char_sz → of_nat n = of_nat 0 :=
|
|
begin
|
|
intro h,
|
|
rw [of_nat_eq_fin_of_ge h],
|
|
reflexivity
|
|
end
|
|
|
|
lemma of_nat_ne_of_ne {n₁ n₂ : nat} (h₁ : n₁ ≠ n₂) (h₂ : n₁ < char_sz) (h₃ : n₂ < char_sz) : of_nat n₁ ≠ of_nat n₂ :=
|
|
begin
|
|
rw [of_nat_eq_of_lt h₂, of_nat_eq_of_lt h₃],
|
|
apply @fin.ne_of_vne _ (fin.mk n₁ h₂) (fin.mk n₂ h₃) h₁
|
|
end
|
|
end char
|