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Proof step 34 from proof bitsxor-is-orand (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 35:
⊦ bits ≠ [] ∧ bits0 = false ' → bitsxor(bits, bits0) = bits
Proof step 36:
bits ≠ [] ∧ false ' = false ', ∀ bits, bits1. # bits1 < # false ' → true → bits = [] ∨ bits1 = [] ∨ bits2int(bitsxor(bits, bits1)) = bits2int(bitsor(bitsand(bitsinvert(bits), bits1), bitsand(bitsinvert(bits1), bits))) ⊦ bits = [], bits2int(bits) = bits2int(bitsor(false ', bits))

Rule argument

name: bitsxor-rec-02 rotate: F subst: [bits0, bits] → [false ', bits]

Additional information

Used terms: false ', bits