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Proof step 8 from proof rm-size-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
a ∈ x0, ∀ a, y. a ∈ x0 → # rmdup(x0 + a ' + y) = # rmdup(x0 + y) ⊦ # (a0 ∈ x0 ∨ a0 ∈ y ⊃ rmdup(x0 + a ' + y);a0 ' + rmdup(x0 + a ' + y)) = # rmdup((a0 ' + x0) + y)

Rule argument

Additional information

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