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Proof step 44 from proof diff-union (previous step)

¬ a ∈ (x0 \ z) + (y \ z), ∀ y0, z0. rmdup(x0 + y0) \ z0 = rmdup((x0 \ z0) + (y0 \ z0)) ⊦ a ' + (rmdup(x0 + y) \ z) = a + rmdup((x0 \ z) + (y \ z)), a ∈ z, a ∈ x0, a ∈ y

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 45:
∀ y0, z0. rmdup(x0 + y0) \ z0 = rmdup((x0 \ z0) + (y0 \ z0)) ⊦ rmdup(x0 + y) \ z = rmdup((x0 \ z) + (y \ z)), a ∈ z, a ∈ x0, a ∈ y

Rule argument

Additional information

Used simplifier rules: diff-in: ⊦ a ∈ x \ y ↔ a ∈ x ∧ ¬ a ∈ y;%in-append: ⊦ a ∈ x + y ↔ ¬ ¬(a ∈ x ∨ a ∈ y); from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%app-08: ⊦ a ' + x = a ' + y ↔ x = y; from specification list%c: ⊦ a + x = a ' + x; from specification list