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Proof step 5 from proof and-true (previous step)

bitsand(bits, bits0) = true ' ⊦ bits0 = [], bits = [], bits = bitsand(bits, bits0) ∧ bits0 = bitsand(bits, bits0), bits ≠ bits.first ' ∧ bits0 ≠ bits0.first '

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
bits = boolvar + bits1, bitsand(bits, bits0) = true ' ⊦ bits0 = [], bits = [], bits = bitsand(bits, bits0) ∧ bits0 = bitsand(bits, bits0), bits ≠ boolvar ' ∧ bits0 ≠ bits0.first '

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0 subst: [bits, boolvar, bits0] → [bits, boolvar, 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: bits, boolvar, bits1