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Proof step 11 from proof modls (previous step)

m0 * n < m0 * m + n0, m < n, n0 < m0 ⊦ m0 * n = m0 * m + n0

User applied rule insert lemma

And obtained the following new goals

Proof step 12:
n0 < m0, m0 * n ≤ m0 * m + n0 ⊦ n ≤ m

Rule argument

spec: nat-mult inst: name: modp seq: n0 < m0, m0 * n ≤ m0 * m + n0 ⊦ n ≤ m subst: [n0, m0, n, m] → [n0, m0, n, m] flags: current, []

Additional information

Used simplifier rules: fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%ref-1: ⊦ ¬ n < n; from specification nat-basic1%lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat%ls-02: ⊦ m < n → ¬ n < m; from specification nat-basic1 Used terms: n0, m0, n, m