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Proof step 27 from proof uint2bits-mod2pot (previous step)

uint2bits((j / 2) % 2 ^ i0) = sgn(false ' + lastn(i→n(i0), uint2bits(j / 2).rest)), 0 ≤ i0, 0 < j, 2 ^ i0 * 2 < j, ∀ j0, i. i→n(j0) < i→n(j) → 0 ≤ i ∧ 2 ^ i < j0 → uint2bits(j0 % 2 ^ i) = sgn(false ' + lastn(i→n(i), uint2bits(j0).rest)) ⊦ ~1 = i0, j = 1, uint2bits(j % (2 ^ i0 * 2)) = sgn(false ' + lastn(i→n(i0), uint2bits(j / 2).rest) + (j % 2 = 1)'), j % 2 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: i % 2 = 1, 0 ≤ i, 0 < j ⊦ i % (2 * j) = (i / 2) % j * 2 + 1 subst: [j, i] → [2 ^ i0, j] rotate: F spec: int-div inst: name: mod-twoodd-01

Additional information

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