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Proof step 35 from proof uint2bits-mod2pot (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 < j ∧ 0 ≤ i → ¬ i % j < 0 subst: [j, i] → [2 ^ i0, j / 2] rotate: F spec: int-div inst: name: mod-zero-01

Additional information

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