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Proof step 1 from proof int2bits-lslen-02 (conclusion)

⊦ i < ~1 ∧ 0 ≤ j → (0 ≤ 2 ^ j + i ↔ # int2bits(i) ≤ i→n(j) + 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ i < ~1 → (# int2bits(i) ≤ m ↔ 0 ≤ i + 2 ^ (n→i(m) - 1))

Rule argument

name: int2bits-lelen-03 rotate: F subst: [m, i] → [i→n(j) + 1, i]

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ n→i(m + n) = n→i(m) + n→i(n);% ⊦ 0 ≤ i → n→i(i→n(i)) = i;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ (* i) + i0 - (* j) = (i - j) + i0;% ⊦ i + 0 = i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: i→n(j) + 1, i