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Proof step 27 from proof bitsinvert-size (previous step)

bits0 = boolvar0 + bits1, bitsinvert(bits0) = (¬ boolvar)' + bits, # sgn(bitsinvert(bits0)) = # sgn(bits0), boolvar ∈ bits0 ⊦ bits0 = [], # sgn(bits0) = # sgn(boolvar ' + bits0), boolvar0 ↔ boolvar

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
# sgn((¬ boolvar)' + bitsinvert(bits1)) = # sgn(boolvar0 ' + bits1), ¬ boolvar0 ↔ ¬ boolvar, boolvar ∈ bits1 ⊦ # sgn(boolvar0 ' + bits1) = # sgn(boolvar ' + boolvar0 ' + bits1), boolvar0 ↔ boolvar

Rule argument

Additional information

Used simplifier rules: inv-append: ⊦ bitsinvert(bits + bits0) = bitsinvert(bits) + bitsinvert(bits0);%inv-one: ⊦ bitsinvert(boolvar ') = (¬ boolvar)';% ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ boolvar ' + bits ≠ [];%⊦ boolvar ' + bits = boolvar0 ' + bits0 ↔ (boolvar ↔ boolvar0) ∧ bits = bits0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar + bits = boolvar ' + bits;