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Proof step 6 from proof sgn-sgn-01 (previous step)

∀ bits1. sgn(sgn(bits0) + bits1) = sgn(bits0 + bits1) ⊦ sgn(sgn(boolvar ' + bits0) + bits1) = sgn((boolvar ' + bits0) + bits1), bits0.first ↔ boolvar, bits0 = []

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

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