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Proof step 8 from proof bitsinvert-size (previous step)

bitsinvert(bits0) = boolvar0 + bits ∧ bitsinvert(bits0) ≠ [], # sgn(bitsinvert(bits0)) = # sgn(bits0) ⊦ # sgn((¬ boolvar)' + bitsinvert(bits0)) = # sgn(boolvar ' + bits0), bits0 = [], boolvar0 ↔ ¬ boolvar

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
bitsinvert(bits0) = boolvar0 ' + bits, # sgn(bitsinvert(bits0)) = # sgn(bits0), (¬ boolvar0) ∈ bits0 ⊦ boolvar0 ↔ ¬ boolvar, bits0 = [], # sgn((¬ boolvar)' + bitsinvert(bits0)) = # sgn(boolvar ' + bits0)

Rule argument

Additional information

Used simplifier rules: inv-empty: ⊦ bitsinvert(bits) = [] ↔ bits = [];%inv-in: ⊦ boolvar ∈ bitsinvert(bits) ↔ (¬ boolvar) ∈ bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' + bits = bits0 → boolvar ∈ bits0; (forward)% ⊦ boolvar + bits = boolvar ' + bits;