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Proof step 1 from proof and-two (conclusion)

⊦ bitsand(boolvar ' + boolvar0 ', boolvar1 ' + boolvar2 ') = (boolvar ∧ boolvar1)' + (boolvar0 ∧ boolvar2)'

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ 1 < # bits ∧ 1 < # bits0 → bitsand(bits, bits0) = bitsand(bits.butlast, bits0.butlast) + (bits.last ∧ bits0.last)

Rule argument

name: and-rec rotate: F subst: [bits0, bits] → [boolvar1 ' + boolvar2 ', boolvar ' + boolvar0 ']

Additional information

Used simplifier rules: and-one: ⊦ bitsand(boolvar ', boolvar0 ') = (boolvar ∧ boolvar0)';% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ (bits + boolvar ').butlast = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ (bits + boolvar ').last ↔ boolvar;% ⊦ bits + boolvar = bits + boolvar ';% ⊦ bits + bits0 = bits + bits1 ↔ bits0 = bits1; Used terms: boolvar1 ' + boolvar2 ', boolvar ' + boolvar0 '