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Proof step 63 from proof bitsand-cast-05 (previous step)

bitsand(false ' + bits0, bits1) = boolvar + bits ∧ bitsand(false ' + bits0, bits1) ≠ [], 1 + # bits0 = # bits1, boolvar ⊦ sgn(bitsand(false ' + bits0, bits1)) = sgn(false ' + bitsand(false ' + bits0, bits1)), bits1 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 64:
1 + # bits0 = # bits1, bitsand(false ' + bits0, bits1) = true ' + bits ⊦ bits1 = []

Rule argument

Additional information

Used simplifier rules: and-notempty-02: ⊦ bits0 ≠ [] → bitsand(boolvar ' + bits, bits0) ≠ [];% ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ sgn(true ' + bits) ≠ false ' + bits0;% ⊦ sgn(false ' + true ' + bits) = false ' + true ' + bits;% ⊦ boolvar ' + bits = bits0 → boolvar ∈ bits0; (forward)% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar + bits = boolvar ' + bits;