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Proof step 4 from proof rm-allsize (previous step)

∀ a0. a0 ∈ a + x0 ↔ a0 ∈ y, ∀ y. (∀ a. a ∈ x0 ↔ a ∈ y) → # rmdup(x0) = # rmdup(y) ⊦ # rmdup(a + x0) = # rmdup(y)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
∀ y. (∀ a. a ∈ x0 ↔ a ∈ y) → # rmdup(x0) = # rmdup(y), ∀ a0. a0 ∈ a ' + x0 ↔ a0 ∈ y ⊦ # rmdup(a ' + x0) = # rmdup(y)

Rule argument

Additional information

Used simplifier rules: ⊦ a + x = a ' + x; (s)