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Proof step 8 from proof band-neg (previous step)

bitsand(int2bits(i), int2bits(j)) = boolvar + bits ∧ bitsand(int2bits(i), int2bits(j)) ≠ [], j < 0, i < 0 ⊦ boolvar

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
bitsand(int2bits(i), int2bits(j)) = false ' + bits, j < 0, i < 0 ⊦

Rule argument

Additional information

Used simplifier rules: and-notempty-09: ⊦ bitsand(int2bits(i), int2bits(i0)) ≠ [];% ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' + bits = bits0 → boolvar ∈ bits0; (forward)% ⊦ boolvar + bits = boolvar ' + bits;