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Proof step 4 from proof and-first (previous step)

⊦ bits0 = [], bitsand(boolvar ' + bits1, bits0).first ↔ boolvar ∧ bits0.first

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 5:
bits0 = boolvar0 + bits ⊦ bits0 = [], bitsand(boolvar ' + bits1, bits0).first ↔ boolvar ∧ boolvar0

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