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Proof step 1 from proof one-01 (conclusion)

⊦ m / 1 = m

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] → [1, m] flags: current, []

Additional information

Used simplifier rules: one: ⊦ m0 * 1 = m0; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%lels-02: ⊦ m ≠ n → (m ≤ n ↔ m < n); from specification nat%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%neq-01: ⊦ m ≠ n → (m < n + 1 ↔ m < n); from specification nat-basic2%ls-02: ⊦ m < n → ¬ n < m; from specification nat-basic1 Used terms: 1, m