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Proof step 4 from proof rm-in-05 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
∀ a, y. a ∈ x0 → rmdup(a ' + x0 + y) = rmdup(x0 + y), a = a0 ∨ a ∈ x0 ⊦ rmdup(a ' + (a0 ' + x0) + y) = rmdup((a0 ' + x0) + y)

Rule argument

Additional information

Used simplifier rules: ⊦ a ∈ b ' ↔ a = b; (s)% ⊦ a ∈ x + y ↔ a ∈ x ∨ a ∈ y; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ a + x = a ' + x; (s)