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Proof step 54 from proof bitsand-cast-05 (previous step)

# bits = # bits1 ⊦ bits = [], sgn(bitsand(bits1, bits)) = sgn(false ' + bitsand(bits, bits1)), bits1 = [], bits.first

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 55:
bits = boolvar + bits0, # bits = # bits1 ⊦ bits = [], sgn(bitsand(bits1, bits)) = sgn(false ' + bitsand(bits, bits1)), bits1 = [], boolvar

Rule argument

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