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Proof step 20 from proof and-sgn (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
bits0 = bits0.first ', ∀ bits1, bits. # bits1 < # bits0 → true → bits = [] ∨ bits1 = [] ∨ sgn(bitsand(sgn(bits), bits1)) = sgn(bitsand(bits, bits1)) ⊦ sgn(bitsand(sgn(boolvar ' + bits2), bits0)) = sgn(bitsand(boolvar ' + bits2, bits0)), bits0 = [], bits0 = true ', bits0 = false ', boolvar ' + bits2 = true ', boolvar ' + bits2 = false ', bits2 = []

Rule argument

Additional information

Used simplifier rules: ⊦ sgn(boolvar ') = boolvar ';% ⊦ boolvar ' = boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ bits + [] = bits;% ⊦ boolvar ' = boolvar0 ' + bits ↔ (boolvar ↔ boolvar0) ∧ bits = [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' + bits ≠ [];% ⊦ boolvar + bits = boolvar ' + bits;