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Proof step 3 from proof rm-in-02 (previous step)

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

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 4:
a0 ∈ x0, ∀ a. a ∈ rmdup(x0) ↔ a ∈ x0 ⊦ a ∈ rmdup(a0 ' + x0) ↔ a = a0 ∨ a ∈ x0
Proof step 10:
∀ a. a ∈ rmdup(x0) ↔ a ∈ x0 ⊦ a0 ∈ x0, a ∈ rmdup(a0 ' + x0) ↔ a = a0 ∨ a ∈ x0

Rule argument

fma: a0 ∈ x0

Additional information

Used formulas: a0 ∈ x0