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Proof step 3 from proof rm-size-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
∀ a, y. a ∈ x0 → # rmdup(x0 + a ' + y) = # rmdup(x0 + y), a = a0 ∨ a ∈ x0 ⊦ # rmdup((a0 ' + x0) + a ' + y) = # rmdup((a0 ' + x0) + y)

Rule argument

Additional information

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