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Proof step 12 from proof bitsor-com (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ bits0 ≠ [] ∧ bits = true ' → bitsor(bits, bits0) = true '
Proof step 14:
¬(bits0 ≠ [] ∧ bits = true '), # bits = 1, ∀ bits, bits1. # bits1 < # bits0 → true → bits ≠ [] ∧ bits1 ≠ [] → bitsor(bits, bits1) = bitsor(bits1, bits) ⊦ bits = [], bits0 = [], bitsor(bits, bits0) = bitsor(bits0, bits), bits0 = true ', bits0 = false ', # bits0 = 1
Proof step 20:
bits0 ≠ [] ∧ bits = true ', # bits = 1, ∀ bits, bits1. # bits1 < # bits0 → true → bits ≠ [] ∧ bits1 ≠ [] → bitsor(bits, bits1) = bitsor(bits1, bits) ⊦ bits = [], bits0 = [], true ' = bitsor(bits0, bits), bits0 = true ', bits0 = false ', # bits0 = 1

Rule argument

name: or-rec-03 rotate: F subst: [bits0, bits] → [bits0, bits]

Additional information

Used terms: bits0, bits