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Proof step 5 from proof rm-allsize (previous step)

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 6:
a ∈ x0, ∀ a0. a0 ∈ a ' + x0 ↔ a0 ∈ y, ∀ y. (∀ a. a ∈ x0 ↔ a ∈ y) → # rmdup(x0) = # rmdup(y) ⊦ # rmdup(a ' + x0) = # rmdup(y)
Proof step 10:
∀ a0. a0 ∈ a ' + x0 ↔ a0 ∈ y, ∀ y. (∀ a. a ∈ x0 ↔ a ∈ y) → # rmdup(x0) = # rmdup(y) ⊦ # rmdup(a ' + x0) = # rmdup(y), a ∈ x0

Rule argument

fma: a ∈ x0

Additional information

Used formulas: a ∈ x0