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Proof step 6 from proof rm-allsize (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
a ∈ x0, ∀ y. (∀ a. a ∈ x0 ↔ a ∈ y) → # rmdup(x0) = # rmdup(y), ∀ a0. a0 ∈ x0 ↔ a0 ∈ y ⊦ # rmdup(x0) = # rmdup(y)

Rule argument

Additional information

Used simplifier rules: rmdup-y: ⊦ a ∈ x → rmdup(a ' + x) = rmdup(x);%a: ⊦ (x + y) + z = x + y + z; from specification list