18 lines
627 B
Text
18 lines
627 B
Text
import standard
|
||
namespace int
|
||
|
||
private lemma sub_nat_nat_elim (m n : ℕ) (P : ℕ → ℕ → ℤ → Prop)
|
||
(hp : ∀i n, P (n + i) n (of_nat i))
|
||
(hn : ∀i m, P m (m + i + 1) (-[1+ i])) :
|
||
P m n (sub_nat_nat m n) :=
|
||
sorry
|
||
|
||
inductive rel_int_nat_nat__ : ℤ → ℕ × ℕ → Prop
|
||
| pos : ∀m p, rel_int_nat_nat__ (of_nat p) (m + p, m)
|
||
| neg : ∀m n, rel_int_nat_nat__ (neg_succ_of_nat n) (m, m + n)
|
||
|
||
lemma rel_sub_nat_nat__ {a b : ℕ} : rel_int_nat_nat__ (sub_nat_nat a b) (a, b) :=
|
||
/- The next statement kills lean -/
|
||
sub_nat_nat_elim a b (λ(a b : ℕ) (i : ℤ), rel_int_nat_nat__ i (a, b)) sorry sorry
|
||
|
||
end int
|