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Proof step 37 from proof or-invandinv (previous step)

∀ bits1, bits0. # bits1 < # bits → true → bits1 = [] ∨ bits0 = [] ∨ bitsor(bits1, bits0) = bitsinvert(bitsand(bitsinvert(bits1), bitsinvert(bits0))) ⊦ bits0 = [], bits = [], bitsor(bits.butlast, bits0.butlast) + (bits.last ∨ bits0.last)' = bitsinvert(bitsand(bitsinvert(bits), bitsinvert(bits0))), bits = bits.first ', bits0 = bits0.first '

User applied rule insert elim lemma

And obtained the following new goals

Proof step 38:
bits = bits2 + boolvar ', ∀ bits1, bits0. # bits1 < # bits → true → bits1 = [] ∨ bits0 = [] ∨ bitsor(bits1, bits0) = bitsinvert(bitsand(bitsinvert(bits1), bitsinvert(bits0))) ⊦ bits0 = [], bits = [], bitsor(bits2, bits0.butlast) + (boolvar ∨ bits0.last)' = bitsinvert(bitsand(bitsinvert(bits), bitsinvert(bits0))), bits = bits.first ', bits0 = bits0.first '

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.last) ∧ bits0 = bits.butlast ↔ bits = bits0 + boolvar ' subst: [bits, boolvar, bits0] → [bits, boolvar, bits2] rotate: T spec: list-last inst: bitlista name: last-elim

Additional information

Used simplifier rules: bits ≠ [] ⊦ (boolvar ↔ bits.last) ∧ bits0 = bits.butlast ↔ bits = bits0 + boolvar '; (elim) Used terms: bits, boolvar, bits2