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Proof step 14 from proof rm-size-02 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
a ∈ y, ∀ a, y. a ∈ y → # rmdup(x0 + a ' + y) = # rmdup(x0 + y) ⊦ 1 + # rmdup(x0 + a ' + y) = 1 + # rmdup(x0 + y), a0 ∈ y, a0 ∈ x0

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ # a ' = 0 +1; (s)% ⊦ #(x + y) = # x + # y; (s)