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Proof step 47 from proof bitsand-app-zeros (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 48:
bitsand(bits + false ' + bits3, false ' + bits4) = [], ∀ bits0, bits, bits2. # bits2 < #(bits4 + boolvar0 ') → true → sgn(bitsand(bits + false ' + bits0, false ' + bits2)) = sgn(bitsand(false ' + bits0, false ' + bits2)) ∨ true ∈ bits ⊦ (boolvar ∧ boolvar0)' = sgn(false ' + (boolvar ∧ boolvar0)'), true ∈ bits, true ∈ bitsand(false ' + bits3, false ' + bits4)

Rule argument

Additional information

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