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Proof step 48 from proof uint2bits-mod2pot (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i;% ⊦ i * j = j * i;% ⊦ i + j = j + i; Used terms: (j / 2) % 2 ^ i0