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Proof step 3 from proof rm-in-04 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list%c: ⊦ a + x = a ' + x; from specification list