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Proof step 70 from proof uint2bits-mod2pot (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 71:
(¬ boolvar) ∈ bits ⊦ sgn(boolvar ' + bits + boolvar0 ') = sgn(boolvar ' + bits) + boolvar0 '
Proof step 72:
¬ (¬ false) ∈ lastn(i→n(i0), uint2bits(j / 2).rest), j % 2 = 0, uint2bits((j / 2) % 2 ^ i0) = sgn(false ' + lastn(i→n(i0), uint2bits(j / 2).rest)), 0 < (j / 2) % 2 ^ i0, 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)) ⊦ uint2bits((j / 2) % 2 ^ i0) + false ' = sgn(false ' + lastn(i→n(i0), uint2bits(j / 2).rest) + false '), ~1 = i0, j = 1

Rule argument

seq: (¬ boolvar) ∈ bits ⊦ sgn(boolvar ' + bits + boolvar0 ') = sgn(boolvar ' + bits) + boolvar0 ' subst: [boolvar0, bits, boolvar] → [false, lastn(i→n(i0), uint2bits(j / 2).rest), false] rotate: F spec: bitopsaux inst: name: sgn-last

Additional information

Used simplifier rules: ⊦ bits + bits0 = bits1 + bits0 ↔ bits = bits1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: false, lastn(i→n(i0), uint2bits(j / 2).rest), false