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Proof step 17 from proof lsucc-01 (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 18:
⊦ 2 * m + 1 < 2 * n ↔ m < n
Proof step 19:
2 * n + 1 < 2 * 2 ^ log2 n * 2 ↔ n < 2 ^ log2 n * 2, 4 * 2 ^ log2 n ≤ 2 * n + 1 ⊦ log2(2 * n + 1) = log2 n + 1, n = 0

Rule argument

spec: nat-mult inst: name: two-succ-04 seq: ⊦ 2 * m + 1 < 2 * n ↔ m < n subst: [m, n] → [n, 2 ^ log2 n * 2] flags:

Additional information

Used terms: n, 2 ^ log2 n * 2