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