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Proof step 26 from proof bitsinvert-size (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 27:
bits0 = boolvar0 + bits1, bitsinvert(bits0) = (¬ boolvar)' + bits, # sgn(bitsinvert(bits0)) = # sgn(bits0), boolvar ∈ bits0 ⊦ bits0 = [], # sgn(bits0) = # sgn(boolvar ' + bits0), boolvar0 ↔ boolvar

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0 subst: [bits, boolvar, bits0] → [bits0, boolvar0, bits1] rotate: T spec: list-data inst: bitlista name: elim-list-c

Additional information

Used simplifier rules: bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0; (elim) Used terms: bits0, boolvar0, bits1