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Proof step 2 from proof and-size-one-01 (previous step)

# bits = # bits1 + 1, bits.first ⊦ bits1 = [], bits0 = [], bitsand(bits, bits0 + bits1) = bits0 + bitsand(bits.rest, bits1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 3:
bits = boolvar + bits2 ∧ bits ≠ [], # bits = # bits1 + 1, boolvar ⊦ bits1 = [], bits0 = [], bitsand(bits, bits0 + bits1) = bits0 + bitsand(bits2, bits1)

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0 subst: [bits, boolvar, bits0] → [bits, boolvar, bits2] rotate: T spec: list-data inst: bitlista name: elim-list-c

Additional information

Used simplifier rules: ⊦ # [] = 0;% ⊦ m + 1 ≠ 0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;%bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0; (elim) Used terms: bits, boolvar, bits2