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Proof step 9 from proof bitsor-ones-false (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

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

Rule argument

name: or-rec-04 rotate: F subst: [bits0, bits] → [false ' + bits1, bits]

Additional information

Used simplifier rules: ⊦ bits = bits + bits0 ↔ bits0 = [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' ≠ [];% ⊦ boolvar ' + bits ≠ [];% ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0; Used terms: false ' + bits1, bits