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Proof step 6 from proof bitsor-zeroes-false (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ 1 < # bits ∧ 1 < # bits0 → bitsor(bits, bits0) = bitsor(bits.butlast, bits0.butlast) + (bits.last ∨ bits0.last)
Proof step 8:
¬(1 < # bits ∧ 1 < #(false ' + bits1)), # bits ≤ 1 + # bits1, ∀ bits1, bits0. # bits0 < # bits → # bits0 ≤ 1 + # bits1 → bits0 = [] ∨ bitsor(bits0, false ' + bits1) = false ' + bits1 ∨ true ∈ bits0 ⊦ bitsor(bits, false ' + bits1) = false ' + bits1, bits = [], true ∈ bits
Proof step 17:
1 < # bits ∧ 1 < #(false ' + bits1), # bits ≤ 1 + # bits1, ∀ bits1, bits0. # bits0 < # bits → # bits0 ≤ 1 + # bits1 → bits0 = [] ∨ bitsor(bits0, false ' + bits1) = false ' + bits1 ∨ true ∈ bits0 ⊦ bitsor(bits.butlast, (false ' + bits1).butlast) + (bits.last ∨ (false ' + bits1).last) = false ' + bits1, bits = [], true ∈ bits

Rule argument

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

Additional information

Used terms: false ' + bits1, bits