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Proof step 3 from proof rmdup-01 (previous step)

∀ x. (∀ a. a ∈ x → a ∈ rmdup(y0)) ↔ (∀ a. a ∈ x → a ∈ y0) ⊦ (∀ a0. a0 ∈ x → a0 ∈ rmdup(a + y0)) ↔ (∀ a0. a0 ∈ x → a0 ∈ a + y0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
∀ x. (∀ a. a ∈ x → a ∈ rmdup(y0)) ↔ (∀ a. a ∈ x → a ∈ y0) ⊦ (∀ a0. a0 ∈ x → a0 ∈ rmdup(a ' + y0)) ↔ (∀ a0. a0 ∈ x → a0 ∈ a ' + y0)

Rule argument

Additional information

Used simplifier rules: c: ⊦ a + x = a ' + x; from specification list