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Proof step 15 from proof int2bits-rec-neg (previous step)

(i * 2 - 1) / 2 < 0, i < 0, i ≤ 0 ⊦ sgn(bitsinvert(uint2bits(~ i)) +1 + false ') = sgn(bitsinvert(uint2bits(~ i)) +1) + false '

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
(¬ boolvar) ∈ bits ⊦ sgn(bits + boolvar ') = sgn(bits) + boolvar '

Rule argument

seq: (¬ boolvar) ∈ bits ⊦ sgn(bits + boolvar ') = sgn(bits) + boolvar ' subst: [boolvar, bits] → [false, bitsinvert(uint2bits(~ i)) +1] rotate: F spec: bitopsaux inst: name: sgn-last-diff

Additional information

Used simplifier rules: ⊦ ¬ true ∈ bits +1 ↔ false; Used terms: false, bitsinvert(uint2bits(~ i)) +1