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Proof step 3 from proof and-rec (previous step)

bits = bits1 + boolvar ' ⊦ bitsand(bits, bits0) = bitsand(bits1, bits0.butlast) + (boolvar ∧ bits0.last)', bits = bits.first ', bits = [], bits0 = bits0.first ', bits0 = []

User applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
bits0 = bits2 + boolvar0 ', bits = bits1 + boolvar ' ⊦ bitsand(bits, bits0) = bitsand(bits1, bits2) + (boolvar ∧ boolvar0)', bits = bits.first ', bits = [], bits0 = bits0.first ', bits0 = []

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.last) ∧ bits0 = bits.butlast ↔ bits = bits0 + boolvar ' subst: [bits, boolvar, bits0] → [bits0, boolvar0, bits2] rotate: T spec: list-last inst: bitlista name: last-elim

Additional information

Used simplifier rules: bits ≠ [] ⊦ (boolvar ↔ bits.last) ∧ bits0 = bits.butlast ↔ bits = bits0 + boolvar '; (elim) Used terms: bits0, boolvar0, bits2