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Proof step 17 from proof rm-size-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
a ∈ x0, ∀ a, y. a ∈ x0 → # rmdup(x0 + a ' + y) = # rmdup(x0 + y) ⊦ 1 + # rmdup(x0 + a ' + y) = # rmdup((a0 ' + x0) + y), a0 ∈ x0, a0 ∈ y

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)