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Proof step 8 from proof and-rec (previous step)

⊦ (bits + boolvar1 ') + boolvar ' = (bits + boolvar1 ').first ', bitsand((bits + boolvar1 ') + boolvar ', bits2 + boolvar0 ') = bitsand(bits + boolvar1 ', bits2) + (boolvar ∧ boolvar0)', bits2 + boolvar0 ' = (bits2 + boolvar0 ').first '

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

seq: ⊦ bits ≠ [] → (∃ bits0, boolvar. bits = bits0 + boolvar ') subst: [bits] → [bits2] rotate: F spec: list inst: bitlista name: lastdiv

Additional information

Used simplifier rules: bitsand-rec: ⊦ bitsand (bits + boolvar ' + boolvar0 ', bits0 + boolvar1 ' + boolvar2 ') = bitsand(bits + boolvar, bits0 + boolvar1) + (boolvar0 ∧ boolvar2);% ⊦ [] + bits = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar '.first ↔ boolvar;% ⊦ boolvar ' = boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ bits ≠ [] → ((bits + bits0).first ↔ bits.first);% ⊦ bits + boolvar ' = bits0 → boolvar ∈ bits0; (forward)% ⊦ bits + boolvar = bits + boolvar ';% ⊦ bits + bits0 = bits + bits1 ↔ bits0 = bits1; Used terms: bits2