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prove assumptions of recursive call
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@ -40,7 +40,19 @@ Nat.div_mod.spec(
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let succ_out = Nat.div_mod.go.succ_quotient(d, 0, Nat.sub(n,d))
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case succ_out {
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refl:
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let ind = Nat.div_mod.spec(Nat.sub(n, d), q.pred, d, r, ?H0, ?H1)
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let H0 = mirror(H0)
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let H0 = case Nat.add.swap(r, d, Nat.mul(q.pred, d)) {
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refl:
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H0
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}: Equal(Nat, n, self.b)
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let H0 = apply((x) Nat.sub(x, d), H0)
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let H0 = case Nat.add.sub(d, Nat.add(r, Nat.mul(q.pred, d))) {
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refl:
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H0
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}: Equal(Nat, Nat.sub(n, d), self.b)
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let H1 = mirror(H1)
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let H1 = Nat.lte.comm.false(d, r, H1)
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let ind = Nat.div_mod.spec(Nat.sub(n, d), q.pred, d, r, H0, H1)
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case ind {
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refl:
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refl
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