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Proof step 15 from proof mod-nle (previous step)

m0 * n0 + n1 < m * n0 + n2, n < n0, m0 < m, m * n0 + n2 ≤ m0 * n + n1, n1 < n0, n1 < n, n2 < n0, n1 + 1 < n0 ⊦ n = 0, n0 = 0, m = 0, n = n0

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

spec: nat inst: name: fle seq: ⊦ m < n ∧ n ≤ n0 → m < n0 subst: [m, n, n0] → [m0 * n0 + n1, m * n0 + n2, m0 * n + n1] flags:

Additional information

Used simplifier rules: modls-03: ⊦ n2 < n ∧ m1 < m ∧ n1 < n → m1 * n + n1 < m * n + n2;%mult-a: ⊦ m0 * m * n = (m0 * m) * n;%mult-c: ⊦ m * n = n * m;%ls: ⊦ m0 * m < m0 * n ↔ m0 ≠ 0 ∧ m < n;%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%l: ⊦ m + n < m + n0 ↔ n < n0; from specification nat-basic2%ls-02: ⊦ m < n → ¬ n < m; from specification nat-basic1 Used terms: m0 * n0 + n1, m * n0 + n2, m0 * n + n1