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Proof step 7 from proof rm-in (previous step)

∀ a, y. a ∈ rmdup(x0 + y) ↔ a ∈ x0 ∨ a ∈ y ⊦ a ∈ rmdup((a0 ' + x0) + y) ↔ a ∈ x0 ∨ a ∈ y, a0 = a

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 8:
∀ a, y. a ∈ rmdup(x0 + y) ↔ a ∈ x0 ∨ a ∈ y ⊦ a ∈ rmdup((a0 ' + x0) + y) ↔ a ∈ x0 ∨ a ∈ y, a0 = a, a ∈ x0

Rule argument

fma: a ∈ x0

Additional information

Used simplifier rules: rm-in-03: ⊦ ¬ a ∈ rmdup(x) → ¬ a ∈ x;% ⊦ a ≠ b → (a ∈ b ' + x ↔ a ∈ x); (s)% ⊦ a ∈ x → a ∈ x + y; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list Used formulas: a ∈ x0