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Proof step 12 from proof bitsand-cast-04 (previous step)

# bits1 < n0 + # bits ⊦ n0 = 0, bits = [], sgn(bitsand(lastn(n0 + # bits, mklist(bits.first, n0) + bits), false ' + bits1)) = sgn(bitsand(bits, false ' + bits1))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
bits = boolvar + bits0, # bits1 < n0 + # bits ⊦ n0 = 0, bits = [], sgn(bitsand(lastn(n0 + # bits, mklist(boolvar, n0) + bits), false ' + bits1)) = sgn(bitsand(bits, false ' + bits1))

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