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Proof step 10 from proof rm-size (previous step)

∀ a, y. # rmdup(x0 + a ' + y) = # rmdup(x0 + y) + 1 ∨ a ∈ x0 ∨ a ∈ y ⊦ # (a0 ∈ x0 ∨ a0 ∈ y ⊃ rmdup(x0 + a ' + y);a0 ' + rmdup(x0 + a ' + y)) = # (a0 ∈ x0 + y ⊃ rmdup(x0 + y);a0 ' + rmdup(x0 + y)) + 1, a = a0, a ∈ x0, a ∈ y

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ a ∈ x + y ↔ a ∈ x ∨ a ∈ y; (s)