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Proof step 6 from proof power-of-2-01 (previous step)

⊦ 2 ^ m = 1, n = 0, 2 * 2 * 2 ^ m / 2 = 2 * 2 ^ m

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
n ≠ 0 ⊦ m % n = 0 → m / n * n = m

Rule argument

spec: nat-div inst: name: mult-02 seq: n ≠ 0 ⊦ m % n = 0 → m / n * n = m subst: [n, m] → [2, 2 ^ m] flags: rewrite

Additional information

Used simplifier rules: 2-pot-mod-01: ⊦ 2 ^ m ≠ 1 → 2 ^ m % 2 = 0;%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult Used terms: 2, 2 ^ m