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Proof step 30 from proof and-sgn (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
∀ bits1, bits. # bits1 < #(bits2 + boolvar ') → true → bits = [] ∨ bits1 = [] ∨ sgn(bitsand(sgn(bits), bits1)) = sgn(bitsand(bits, bits1)) ⊦ bits = [], sgn(bitsand(sgn(bits), bits2 + boolvar ')) = sgn(bitsand(bits.butlast, bits2) + (bits.last ∧ boolvar)'), bits = bits.first ', bits2 + boolvar ' = (bits2 + boolvar ').first '

Rule argument

Additional information

Used simplifier rules: ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bits + boolvar ' ≠ [];