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Proof step 2 from proof bitsand-app-true (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

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

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0 subst: [bits, boolvar, bits0] → [bits1, boolvar, bits2] 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: bits1, boolvar, bits2