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Proof step 12 from proof divi-add (previous step)

m * n = m * n1 + n0 ⊦ m * (n - n1) = n0

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 13:
m2 < m1 ⊦ (* m2) * m = (* m1) * m + n0 ↔ (m1 - m2) * m + n0 = 0
Proof step 14:
m * n = m * n1 + n0 ⊦ n < n1, m * (n - n1) = n0

Rule argument

spec: nat-mult inst: name: numeral-08 seq: m2 < m1 ⊦ (* m2) * m = (* m1) * m + n0 ↔ (m1 - m2) * m + n0 = 0 subst: [m2, m1, m, n0] → [n, n1, m, n0] flags:

Additional information

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