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Proof step 20 from proof lsucc-01 (previous step)

4 * 2 ^ log2 n ≤ 2 * n + 1, 2 ^ log2 n * 2 ≤ n ⊦ n = 0, log2(2 * n + 1) = log2 n + 1

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: nat-pot inst: name: ltwo-05 seq: ⊦ n < 2 * 2^ log2 n subst: [n] → [n] flags: current, []

Additional information

Used simplifier rules: pot2-def: ⊦ 2^ m = 2 ^ m;%two-pot-zero: ⊦ 2 ^ n ≠ 0;%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%mult-c: ⊦ m * n = n * m; from specification nat-mult%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%two-zero-01: ⊦ 2 * m = 0 ↔ m = 0; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%f: ⊦ m < n → n ≠ 0; from specification nat-basic1%ref-1: ⊦ ¬ n < n; from specification nat-basic1 Used terms: n