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Proof step 18 from proof bitsand-app-zeros (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
∀ bits0, bits, bits2. # bits2 < # [] → true → sgn(bitsand(bits + false ' + bits0, false ' + bits2)) = sgn(bitsand(false ' + bits0, false ' + bits2)) ∨ true ∈ bits ⊦ sgn(bitsand(bits + false ' + bits0, false ')) = false ', true ∈ bits

Rule argument

Additional information

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