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Proof step 27 from proof bitsxor-is-orand (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
∀ bits, bits1. # bits1 < # bits0 → true → bits = [] ∨ bits1 = [] ∨ bits2int(bitsxor(bits, bits1)) = bits2int(bitsor(bitsand(bitsinvert(bits), bits1), bitsand(bitsinvert(bits1), bits))) ⊦ bits0 = [], # bits0 = 1, bits0 = false ', bits0 = true ', bits2int(bitsxor(false ', bits0)) = bits2int(bitsor(bits0, false '))

Rule argument

Additional information

Used simplifier rules: ⊦ bitsinvert(bits) = [] ↔ bits = [];