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Proof step 9 from proof bitsor-zeroes-true (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ bits ≠ [] ∧ bits0 = true ' → bitsor(bits, bits0) = true '
Proof step 11:
¬(bits ≠ [] ∧ true ' + bits1 = true '), ∀ bits1, bits0. # bits0 < # bits → true → bits0 = [] ∨ bitsor(bits0, true ' + bits1) = true ' + bits1 ∨ true ∈ bits0 ⊦ bitsor(bits, true ' + bits1) = true ' + bits1, bits = [], true ∈ bits, # bits ≠ 1 ∧ bits1 ≠ []

Rule argument

name: or-rec-01 rotate: F subst: [bits0, bits] → [true ' + bits1, bits]

Additional information

Used terms: true ' + bits1, bits