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Proof step 41 from proof bib-neg-high (previous step)

i0 < 0 ⊦ b2i(i2b(bits2int(sgn(bitsinvert(uint2bits(~ i0)) + true ').last ' + false ' + false ' + false ' + false ' + false ' + false ' + false '))) = ~128, i0 = 0, i0 * 256 ≠ ~128 ∧ sgn(bitsinvert(uint2bits(~ i0)) + true ').last

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 42:
(¬ boolvar) ∈ bits ⊦ sgn(bits + boolvar ') = sgn(bits) + boolvar '
Proof step 43:
(¬ true) ∈ bitsinvert(uint2bits(~ i0)), i0 < 0 ⊦ b2i(i2b(bits2int((sgn(bitsinvert(uint2bits(~ i0))) + true ').last ' + false ' + false ' + false ' + false ' + false ' + false ' + false '))) = ~128, i0 = 0, i0 * 256 ≠ ~128 ∧ (sgn(bitsinvert(uint2bits(~ i0))) + true ').last

Rule argument

spec: bitopsaux inst: name: sgn-last-diff seq: (¬ boolvar) ∈ bits ⊦ sgn(bits + boolvar ') = sgn(bits) + boolvar ' subst: [boolvar, bits] → [true, bitsinvert(uint2bits(~ i0))] flags: rewrite

Additional information

Used simplifier rules: inv-in-01: ⊦ false ∈ bitsinvert(bits) ↔ true ∈ bits; from specification bitopsaux%uint2bits-onein-01: ⊦ j < 0 → true ∈ uint2bits(~ j); from specification int2bits Used terms: true, bitsinvert(uint2bits(~ i0))