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Proof step 5 from proof in-01-02 (previous step)

a0 < b, ∀ a, b. (a ∈ ins≤(b, x0) ↔ a ∈ x0) ∨ a = b ⊦ a = b, a ∈ ins≤(b, a0 ' + x0) ↔ a = a0 ∨ a ∈ x0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
a0 < b, ∀ a, b. (a ∈ ins≤(b, x0) ↔ a ∈ x0) ∨ a = b ⊦ a = b, a ∈ ins≤(b, x0) ↔ a ∈ x0, a = a0

Rule argument

Additional information

Used simplifier rules: ins-n: ⊦ b < a → ins≤(a, b ' + x) = b + ins≤(a, x);%in-rec: ⊦ a ∈ b ' + x ↔ ¬ ¬(a = b ∨ a ∈ x); from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%c: ⊦ a + x = a ' + x; from specification list