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Proof step 86 from proof and-sgn (previous step)

(¬ boolvar0) ∈ bits0, (¬ boolvar0 ∨ ¬ boolvar) ∈ bitsand(bits0, bits2), ∀ bits1, bits. # bits1 < #(bits2 + boolvar ') → true → bits = [] ∨ bits1 = [] ∨ sgn(bitsand(sgn(bits), bits1)) = sgn(bitsand(bits, bits1)) ⊦ bits0 = [], sgn(bitsand(sgn(bits0), bits2) + (boolvar0 ∧ boolvar)') = sgn(bitsand(bits0, bits2)) + (boolvar0 ∧ boolvar)', bits2 = [], bits0 + boolvar0 ' = bits0.first ', bits2 + boolvar ' = bits2.first '

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: (¬ boolvar) ∈ bits ⊦ sgn(bits + boolvar ') = sgn(bits) + boolvar ' subst: [boolvar, bits] → [boolvar0 ∧ boolvar, bitsand(sgn(bits0), bits2)] rotate: F spec: bitopsaux inst: name: sgn-last-diff

Additional information

Used terms: boolvar0 ∧ boolvar, bitsand(sgn(bits0), bits2)