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Proof step 10 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), a ∈ x0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
∀ y. (∀ a. a ∈ x0 ↔ a ∈ y) → # rmdup(x0) = # rmdup(y), ∀ a0. a0 ∈ a ' + x0 ↔ a0 ∈ y ⊦ 1 + # rmdup(x0) = # rmdup(y), a ∈ x0

Rule argument

Additional information

Used simplifier rules: rmdup-n: ⊦ ¬ a ∈ x → rmdup(a ' + x) = a + rmdup(x);% ⊦ # a ' = 0 +1; (s)% ⊦ #(x + y) = # x + # y; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ a + x = a ' + x; (s)