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Proof step 12 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(bitsand(false ' + bits0, false ' + bits1)), false ' + bits1 = true ', true ∈ bits, bits0 ≠ [] ∧ bits1 ≠ []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
∀ bits0, bits, bits2. # bits2 < # bits1 → true → sgn(bitsand(bits + false ' + bits0, false ' + bits2)) = sgn(bitsand(false ' + bits0, false ' + bits2)) ∨ true ∈ bits ⊦ bits1 = [], false ' + bits1 = true ', sgn(bitsand(bits + false ', false ' + bits1)) = false ', true ∈ bits

Rule argument

Additional information

Used simplifier rules: and-zero-01: ⊦ bitsand(false ', boolvar ' + bits) = false ';% ⊦ sgn(boolvar ') = boolvar ';% ⊦ bits + [] = bits;% ⊦ bits = bits + bits0 ↔ bits0 = [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' ≠ [];% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];