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Proof step 2 from proof and-notone-03 (previous step)

bitsand(bits, bits0) = true ' + bits1, true ∈ bitsand(bits, bits0) ⊦ bits0 = [], bits = [], bits0.first

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

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

Additional information

Used simplifier rules: and-notone-01: ⊦ bits ≠ [] → bitsand(bits, false ' + bits0) ≠ true ' + bits1;% ⊦ boolvar + bits = boolvar ' + bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;%bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0; (elim) Used terms: bits0, boolvar, bits2