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Proof step 4 from proof sgn-last-diff (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 5:
bits = boolvar0 + bits0, (¬ boolvar) ∈ bits ⊦ sgn(bits + boolvar ') = sgn(bits) + boolvar ', bits = [], (¬ boolvar0) ∈ bits0

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