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Proof step 46 from proof bitsxor-is-orand (previous step)

∀ bits, bits1. # bits1 < # bits0 → true → bits = [] ∨ bits1 = [] ∨ bits2int(bitsxor(bits, bits1)) = bits2int(bitsor(bitsand(bitsinvert(bits), bits1), bitsand(bitsinvert(bits1), bits))) ⊦ bits0 = [], bits = [], bits2int(bitsxor(bits, bits0)) = bits2int(bitsor(bitsand(bitsinvert(bits).butlast, bits0.butlast) + (bitsinvert(bits).last ∧ bits0.last)', bitsand(bitsinvert(bits0), bits))), # bits = 1, # bits0 = 1

User applied rule insert elim lemma

And obtained the following new goals

Proof step 47:
bits0 = bits2 + boolvar ', ∀ bits, bits1. # bits1 < # bits0 → true → bits = [] ∨ bits1 = [] ∨ bits2int(bitsxor(bits, bits1)) = bits2int(bitsor(bitsand(bitsinvert(bits), bits1), bitsand(bitsinvert(bits1), bits))) ⊦ bits0 = [], bits = [], bits2int(bitsxor(bits, bits0)) = bits2int(bitsor(bitsand(bitsinvert(bits).butlast, bits2) + (bitsinvert(bits).last ∧ boolvar)', bitsand(bitsinvert(bits0), bits))), # bits = 1, # bits0 = 1

Rule argument

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