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Proof step 5 from proof and-rec (previous step)

⊦ bitsand(bits1 + boolvar ', bits2 + boolvar0 ') = bitsand(bits1, bits2) + (boolvar ∧ boolvar0)', bits1 + boolvar ' = (bits1 + boolvar ').first ', bits2 + boolvar0 ' = (bits2 + boolvar0 ').first '

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 6:
⊦ bits ≠ [] → (∃ bits0, boolvar. bits = bits0 + boolvar ')
Proof step 7:
bits1 ≠ [] → (∃ bits0, boolvar. bits1 = bits0 + boolvar ') ⊦ bitsand(bits1 + boolvar ', bits2 + boolvar0 ') = bitsand(bits1, bits2) + (boolvar ∧ boolvar0)', bits1 + boolvar ' = (bits1 + boolvar ').first ', bits2 + boolvar0 ' = (bits2 + boolvar0 ').first '

Rule argument

seq: ⊦ bits ≠ [] → (∃ bits0, boolvar. bits = bits0 + boolvar ') subst: [bits] → [bits1] rotate: F spec: list inst: bitlista name: lastdiv

Additional information

Used terms: bits1