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Proof step 12 from proof bitsor-mklist-in (previous step)

∀ bits, boolvar0, boolvar, n, bits1. # bits1 < 1 → true → n = 0 ∨ bits1 = [] ∨ (boolvar ∈ bitsor(mklist(boolvar0, n) + bits, bits1) ↔ boolvar ∈ bitsor(boolvar0 ' + bits, bits1)) ⊦ n = 0, boolvar ∈ bitsor(mklist(boolvar0, n) + bits, false ') ↔ boolvar ∈ bitsor(boolvar0 ' + bits, false ')

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ bits ≠ [] ∧ bits0 = false ' → bitsor(bits, bits0) = bits
Proof step 14:
mklist(boolvar0, n) + bits ≠ [] ∧ false ' = false ', ∀ bits, boolvar0, boolvar, n, bits1. # bits1 < 1 → true → n = 0 ∨ bits1 = [] ∨ (boolvar ∈ bitsor(mklist(boolvar0, n) + bits, bits1) ↔ boolvar ∈ bitsor(boolvar0 ' + bits, bits1)) ⊦ n = 0, boolvar ∈ mklist(boolvar0, n) + bits ↔ boolvar ∈ bitsor(boolvar0 ' + bits, false ')

Rule argument

name: or-rec-02 rotate: F subst: [bits0, bits] → [false ', mklist(boolvar0, n) + bits]

Additional information

Used simplifier rules: ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: false ', mklist(boolvar0, n) + bits