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Proof step 26 from proof sgn-last-04 (previous step)

bits0 + boolvar0 ' = boolvar1 ' + bits, boolvar0 ∈ bits, boolvar1 ∈ bits0, ∀ boolvar. (¬ boolvar) ∈ bits0 → sgn(bits0 + boolvar ') = sgn(bits0) + boolvar ' ⊦ bits0 = [], sgn(boolvar1 ' + bits) = sgn(boolvar1 ' + bits0) + boolvar0 ', bits0.first ↔ ¬ boolvar1, ¬ (¬ boolvar0) ∈ bits0 ∧ ¬(¬ boolvar0 ↔ boolvar1)

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, boolvar2, 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, boolvar2, bits1