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Proof step 25 from proof bitsand-app-zeros (previous step)

bits1 = bits4 + boolvar0 ', ∀ bits0, bits, bits2. # bits2 < # bits1 → true → sgn(bitsand(bits + false ' + bits0, false ' + bits2)) = sgn(bitsand(false ' + bits0, false ' + bits2)) ∨ true ∈ bits ⊦ bits1 = [], sgn(bitsand(bits + false ' + bits3 + boolvar ', false ' + bits1)) = sgn(bitsand(false ' + bits3, false ' + bits4) + (boolvar ∧ boolvar0)'), true ∈ bits

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 26:
∀ bits0, bits, bits2. # bits2 < #(bits4 + boolvar0 ') → true → sgn(bitsand(bits + false ' + bits0, false ' + bits2)) = sgn(bitsand(false ' + bits0, false ' + bits2)) ∨ true ∈ bits ⊦ sgn(bitsand(bits + false ' + bits3 + boolvar ', false ' + bits4 + boolvar0 ')) = sgn(bitsand(false ' + bits3, false ' + bits4) + (boolvar ∧ boolvar0)'), true ∈ bits

Rule argument

Additional information

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