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Proof step 8 from proof lls-02 (previous step)

m < 2 ^ (m1 + 1), 2 ^ m1 ≤ m, n ≤ m, log2 m < log2 n, 2 ^ m0 ≤ n, n < 2 ^ (m0 + 1), 2 ^ m0 ≤ m, n < 2 ^ (m1 + 1), m0 ≤ m1 ⊦ n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ 2^ m ≤ n ∧ n < 2^ m +1 → log2 n = m
Proof step 10:
2^ m0 ≤ n ∧ n < 2^ m0 +1, m < 2 ^ (m1 + 1), 2 ^ m1 ≤ m, n ≤ m, log2 m < m0, 2 ^ m0 ≤ n, n < 2 ^ (m0 + 1), 2 ^ m0 ≤ m, n < 2 ^ (m1 + 1), m0 ≤ m1 ⊦ n = 0

Rule argument

spec: nat-pot inst: name: Log2def seq: ⊦ 2^ m ≤ n ∧ n < 2^ m +1 → log2 n = m subst: [m, n] → [m0, n] flags: rewrite, current

Additional information

Used simplifier rules: pot2-def: ⊦ 2^ m = 2 ^ m;%succ: ⊦ m +1 = m + 1; from specification nat-basic2 Used terms: m0, n