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Proof step 39 from proof or-invandinv (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 40:
bits0 = bits + boolvar0 ', ∀ bits1, bits0. # bits1 < #(bits2 + boolvar ') → true → bits1 = [] ∨ bits0 = [] ∨ bitsor(bits1, bits0) = bitsinvert(bitsand(bitsinvert(bits1), bitsinvert(bits0))) ⊦ bits2 + boolvar ' = (bits2 + boolvar ').first ', bits0 = bits0.first ', bits0 = [], bitsor(bits2, bits) + (boolvar ∨ boolvar0)' = bitsinvert(bitsand(bitsinvert(bits2) + (¬ boolvar)', bitsinvert(bits0)))

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.last) ∧ bits0 = bits.butlast ↔ bits = bits0 + boolvar ' subst: [bits, boolvar, bits0] → [bits0, boolvar0, bits] 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: bits0, boolvar0, bits