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Proof step 19 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 = 1, bits0 = false ', bits0 = true ', bits0 = [], bits2int(bitsxor(true ', bits0)) = bits2int(bitsor(false ', bitsinvert(bits0)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ bits0 ≠ [] ∧ bits = false ' → bitsor(bits, bits0) = bits0
Proof step 21:
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 = 1, bits0 = false ', bits0 = true ', bits0 = [], bits2int(bitsxor(true ', bits0)) = bits2int(bitsinvert(bits0))

Rule argument

name: or-rec-04 rotate: F subst: [bits0, bits] → [bitsinvert(bits0), false ']

Additional information

Used simplifier rules: ⊦ bitsinvert(bits) = [] ↔ bits = []; Used terms: bitsinvert(bits0), false '