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

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

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

spec: nat-basic1 inst: name: trans-1 seq: ⊦ n < n0 ∧ n0 < n1 → n < n1 subst: [n, n0, n1] → [m * n0 + n2, m0 * n0 + n1, m * n0 + n2] 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;%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%l-04: ⊦ m + m0 < n + n0 → (¬ m + m0 < n + n0 ↔ false); from specification nat-basic2%l: ⊦ m + n < m + n0 ↔ n < n0; from specification nat-basic2%ref-1: ⊦ ¬ n < n; from specification nat-basic1 Used terms: m * n0 + n2, m0 * n0 + n1, m * n0 + n2