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Proof step 32 from proof and-sgn (previous step)

bits = bits0 + boolvar0 ', ∀ 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(bits0, bits2) + (boolvar0 ∧ boolvar)'), bits = bits.first ', bits2 + boolvar ' = (bits2 + boolvar ').first '

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 33:
∀ bits1, bits. # bits1 < #(bits2 + boolvar ') → true → bits = [] ∨ bits1 = [] ∨ sgn(bitsand(sgn(bits), bits1)) = sgn(bitsand(bits, bits1)) ⊦ sgn(bitsand(sgn(bits0 + boolvar0 '), bits2 + boolvar ')) = sgn(bitsand(bits0, bits2) + (boolvar0 ∧ boolvar)'), bits0 + boolvar0 ' = (bits0 + boolvar0 ').first ', bits2 + boolvar ' = (bits2 + boolvar ').first '

Rule argument

Additional information

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