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Proof step 9 from proof fst-nle (previous step)

m.1 ≤ m, m0 * m + n ≤ m.1, m0 * m + n ≤ m ⊦ m0 = 1, m0 = 0, m = 0 ∧ n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: nat-mult inst: name: numeral-32 seq: m2 ≠ 0 ⊦ (* m2) * m + n ≤ m ↔ (m2 - 1) * m + n = 0 subst: [n, m, m2] → [n, m, m0] flags: rewrite

Additional information

Used simplifier rules: z-01: ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%zero-06: ⊦ m ≠ 0 → (m * n = 0 ↔ n = 0); from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%add-base: ⊦ n + 0 = n; from specification nat-basic2%le-04: ⊦ m ≤ n → (n * n0 ≤ m ↔ n0 = 0 ∨ n0 = 1 ∧ m = n ∨ n = 0); from specification nat-mult Used terms: n, m, m0