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Proof step 6 from proof fill-sgn (previous step)

# sgn(bits) ≤ # bits ⊦ bits = [], mklist(bits.first, # bits - # sgn(bits)) + sgn(bits) = bits

Heuristic var elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 7:
bits = boolvar + bits0, # sgn(bits) ≤ # bits ⊦ bits = [], mklist(boolvar, # bits - # sgn(bits)) + sgn(bits) = bits

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