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Proof step 1 from proof and-rec-05 (conclusion)

⊦ bitsand(bits + boolvar ' + true ', bits0 + boolvar1 ' + true ') = bitsand(bits + boolvar, bits0 + boolvar1) + true '

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ bitsand(bits + boolvar ' + boolvar0 ', bits0 + boolvar1 ' + boolvar2 ') = bitsand(bits + boolvar, bits0 + boolvar1) + (boolvar0 ∧ boolvar2)

Rule argument

name: bitsand-rec rotate: F subst: [boolvar2, boolvar1, bits0, boolvar0, boolvar, bits] → [true, boolvar1, bits0, true, boolvar, bits]

Additional information

Used simplifier rules: ⊦ bits + boolvar = bits + boolvar ';% ⊦ bits + bits0 = bits + bits1 ↔ bits0 = bits1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: true, boolvar1, bits0, true, boolvar, bits