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Proof step 13 from proof uint2bits-2pot-neg-mone (previous step)

0 < j, 0 < i, ∀ j, i0. i→n(i0) < i→n(i) → 0 < j ∧ 0 < i0 → uint2bits(j * 2 ^ i0 - 1) = uint2bits(j - 1) + mklist(true, i→n(i0)) ⊦ 2 ^ (i - 1) * j = 1, uint2bits(2 ^ (i - 1) * j - 1) + ((2 * 2 ^ (i - 1) * j - 1) % 2 ≠ 0)' = uint2bits(j - 1) + mklist(true, i→n(i))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 < i → (2 * i - 1) % 2 = 1 subst: [i] → [2 ^ (i - 1) * j] rotate: F spec: int-div inst: name: mod-two-pred

Additional information

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