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Proof step 7 from proof mod-le-03 (previous step)

n + m / n * n ≤ m ⊦ n = 0

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: inst: name: Divdef seq: ⊦ n ≠ 0 → m / n * n ≤ m ∧ m < (m / n)+1 * n subst: [n, m] → [n, m] flags: current, []

Additional information

Used simplifier rules: succ: ⊦ m +1 = m + 1; from specification nat-basic2%rsucc-02: ⊦ m * (n + 1) = m * n + m; from specification nat-mult%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%le-ls-simp: ⊦ m ≤ n → (n < m ↔ false); from specification nat Used terms: n, m