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Proof step 6 from proof or-rec (previous step)

⊦ bitsor(bits1 + boolvar ', bits + boolvar0 ') = bitsor(bits1, bits) + (boolvar ∨ boolvar0)', bits1 + boolvar ' = (bits1 + boolvar ').first ', bits + boolvar0 ' = (bits + boolvar0 ').first '

User applied rule insert lemma

And obtained the following new goals

Rule argument

name: bitsor-rec subst: [bits, boolvar, boolvar0, bits0, boolvar1, boolvar2] → [bits1.butlast, bits1.last, boolvar, bits.butlast, bits.last, boolvar0]

Additional information

Used simplifier rules: ⊦ boolvar ' = boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ boolvar '.first ↔ boolvar;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ [] + bits = bits;%bits ≠ [] ⊦ bits.butlast + bits.last ' = bits;% ⊦ bits + boolvar = bits + boolvar '; Used terms: bits1.butlast, bits1.last, boolvar, bits.butlast, bits.last, boolvar0