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Proof step 38 from proof bitsand-cast-05 (previous step)

# bits0 = 1 + # bits1, # bits1 < # bits0, # bits1 < # bits2 + # bits0 ⊦ bits2 + bits0 = [], # bits1 = # bits2 + # bits0, bits0 = [], bits1 = [], sgn(bitsand(bits0.rest, false ' + bits1)) = sgn(bitsand(bits0, false ' + bits1))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 39:
bits0 = boolvar + bits, # bits0 = 1 + # bits1, # bits1 < # bits0, # bits1 < # bits2 + # bits0 ⊦ bits2 + bits0 = [], # bits1 = # bits2 + # bits0, bits0 = [], bits1 = [], sgn(bitsand(bits, false ' + bits1)) = sgn(bitsand(bits0, false ' + bits1))

Rule argument

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