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Proof step 52 from proof uint2bits-mod2pot (previous step)

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)) ⊦ j = 1, ~1 = i0, (j / 2) % 2 ^ i0 = 0, sgn(false ' + lastn(i→n(i0), uint2bits(j / 2).rest)) + true ' = 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: boolvar ↔ ¬ boolvar0 ⊦ sgn(boolvar ' + bits + boolvar0 ') = sgn(boolvar ' + bits) + boolvar0 ' subst: [boolvar0, bits, boolvar] → [true, lastn(i→n(i0), uint2bits(j / 2).rest), false] rotate: F spec: bitopsaux inst: name: sgn-last-01

Additional information

Used terms: true, lastn(i→n(i0), uint2bits(j / 2).rest), false