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Proof step 27 from proof rm-size-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
∀ a, y. a ∈ x0 → # rmdup(x0 + a ' + y) = # rmdup(x0 + y) ⊦ # rmdup(x0 + a0 ' + y) = # (a0 ∈ y ⊃ rmdup(x0 + y);a0 ' + rmdup(x0 + y)), a0 ∈ x0

Rule argument

Additional information

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