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Proof step 8 from proof uint2bits-add-high-02 (previous step)

0 ≤ j0 + 2 ^ i, 2 ^ (i - 1) + j0 < 0, 0 < i, j0 < 0 ⊦ sgn(int2bits(j0).rest) = sgn(false ' + fillsgn(i→n(i), int2bits(j0).rest))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
bits ≠ [], bits.first ↔ boolvar ⊦ sgn(boolvar ' + bits) = sgn(bits)
Proof step 10:
¬(fillsgn(i→n(i), int2bits(j0).rest) ≠ [] ∧ (fillsgn(i→n(i), int2bits(j0).rest).first ↔ false)), 0 ≤ j0 + 2 ^ i, 2 ^ (i - 1) + j0 < 0, 0 < i, j0 < 0 ⊦ sgn(int2bits(j0).rest) = sgn(false ' + fillsgn(i→n(i), int2bits(j0).rest))
Proof step 20:
fillsgn(i→n(i), int2bits(j0).rest) ≠ [] ∧ (fillsgn(i→n(i), int2bits(j0).rest).first ↔ false), 0 ≤ j0 + 2 ^ i, 2 ^ (i - 1) + j0 < 0, 0 < i, j0 < 0 ⊦ sgn(int2bits(j0).rest) = sgn(fillsgn(i→n(i), int2bits(j0).rest))

Rule argument

seq: bits ≠ [], bits.first ↔ boolvar ⊦ sgn(boolvar ' + bits) = sgn(bits) subst: [bits, boolvar] → [fillsgn(i→n(i), int2bits(j0).rest), false] rotate: F spec: bitopsaux inst: name: sgn-rec-01

Additional information

Used terms: fillsgn(i→n(i), int2bits(j0).rest), false