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Proof step 8 from proof bitsor-app (previous step)

# bits4 + 1 = # bits2, ∀ bits1, bits, bits2, bits3. # bits3 < #(bits4 + boolvar ') → true → # bits3 = # bits2 ∧ bits ≠ [] ∧ bits3 ≠ [] ∧ bits1 ≠ [] ∧ bits2 ≠ [] → bitsor(bits + bits3, bits1 + bits2) = bitsor(bits, bits1) + bitsor(bits3, bits2) ⊦ bits = [], bits1 = [], bits2 = [], bitsor(bits + bits4, bits1 + bits2.butlast) + (boolvar ∨ bits2.last)' = bitsor(bits, bits1) + bitsor(bits4 + boolvar ', bits2), # bits + # bits2 = 0, # bits1 + # bits2 = 0

User applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
bits2 = bits0 + boolvar0 ', # bits4 + 1 = # bits2, ∀ bits1, bits, bits2, bits3. # bits3 < #(bits4 + boolvar ') → true → # bits3 = # bits2 ∧ bits ≠ [] ∧ bits3 ≠ [] ∧ bits1 ≠ [] ∧ bits2 ≠ [] → bitsor(bits + bits3, bits1 + bits2) = bitsor(bits, bits1) + bitsor(bits3, bits2) ⊦ bits = [], bits1 = [], bits2 = [], bitsor(bits + bits4, bits1 + bits0) + (boolvar ∨ boolvar0)' = bitsor(bits, bits1) + bitsor(bits4 + boolvar ', bits2), # bits + # bits2 = 0, # bits1 + # bits2 = 0

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.last) ∧ bits0 = bits.butlast ↔ bits = bits0 + boolvar ' subst: [bits, boolvar, bits0] → [bits2, boolvar0, bits0] 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: bits2, boolvar0, bits0