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Proof step 1 from proof mod-neq-05 (conclusion)

⊦ n ≠ 0 → m * n + m ≠ m0 * n + m0 + n

User applied rule insert lemma

And obtained the following new goals

Proof step 2:
⊦ n1 < n ∧ n0 < n ∧ n0 ≠ n1 → m0 * n + n0 ≠ m * n + n1

Rule argument

spec: nat-mult inst: name: mod-neq-04 seq: ⊦ n1 < n ∧ n0 < n ∧ n0 ≠ n1 → m0 * n + n0 ≠ m * n + n1 subst: [n1, n, n0, m0, m] → [n, n + 1, 0, m, m0] flags: current, []

Additional information

Used simplifier rules: rsucc-01: ⊦ (m + 1) * n = m * n + n;%mult-a: ⊦ m0 * m * n = (m0 * m) * n;%mult-c: ⊦ m * n = n * m;%s: ⊦ m < n + 1 ↔ ¬ n < m; from specification nat-basic2%ref-1: ⊦ ¬ n < n; from specification nat-basic1%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%zero: ⊦ 0 < m ↔ m ≠ 0; from specification nat-basic1%oz: ⊦ m + 1 ≠ 0; from specification nat-basic2%add-base: ⊦ n + 0 = n; from specification nat-basic2 Used terms: n, n + 1, 0, m, m0