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Proof step 5 from proof sgn-base-04 (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
bits = boolvar0 + bits0 ⊦ sgn(boolvar ' + bits) = boolvar ' + bits, boolvar0 ↔ ¬ boolvar, bits = [], boolvar ∈ bits

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0 subst: [bits, boolvar, bits0] → [bits, boolvar0, bits0] 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: bits, boolvar0, bits0