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Proof step 15 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)) ⊦ mklist(boolvar0, n) + bits = [], n = 0, boolvar ∈ mklist(boolvar0, n) ∨ boolvar ∈ bits ↔ boolvar ∈ bitsor(boolvar0 ' + bits, false ')

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

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