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Proof step 7 from proof sgn-length (previous step)

1 + # bits0 < # sgn(boolvar ' + bits0), # sgn(bits0) ≤ # bits0 ⊦ bits0.first ↔ boolvar, bits0 = []

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
bits0 = boolvar0 + bits, 1 + # bits0 < # sgn(boolvar ' + bits0), # sgn(bits0) ≤ # bits0 ⊦ boolvar0 ↔ boolvar, bits0 = []

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0 subst: [bits, boolvar, bits0] → [bits0, boolvar0, 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, boolvar0, bits