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Proof step 71 from proof band-011x-pos (previous step)

bits2uint(bits) = i1 % 2 ^ i0, bitsand(false ' + mklist(true, i→n(i0)), uint2bits(i1)) = false ' + bits, 0 ≤ i0, 0 < i1, ∀ j0, i. i→n(j0) < i→n(i1 * 2 + 1) → 0 ≤ j0 ∧ 0 ≤ j0 ∧ 0 ≤ i → bits2int(bitsand(false ' + mklist(true, i→n(i)), uint2bits(j0))) = j0 % 2 ^ i ⊦ bits2uint(bits) * 2 + 1 = (i1 * 2 + 1) % (2 ^ i0 * 2), ~1 = i0, i1 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: 0 ≤ i, 0 < j ⊦ (2 * i + 1) % (2 * j) = i % j * 2 + 1 subst: [j, i] → [2 ^ i0, i1] rotate: F spec: int-div inst: name: mod-twoodd

Additional information

Used simplifier rules: ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ 0 < i → (0 < i ^ j ↔ i = 1 ∨ 0 ≤ j);% ⊦ i < j → ¬ j < i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i + j = i + i0 ↔ j = i0;% ⊦ 0 < i → (i * j = i * j0 ↔ j = j0);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i * j = j * i;% ⊦ i + j = j + i; Used terms: 2 ^ i0, i1