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Proof step 5 from proof rm-in-04 (previous step)

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

Heuristic cut applied rule cut formula

And closed the goal!

Rule argument

fma: a ∈ (a0 ' + x0) + y

Additional information

Used simplifier rules: rmdup-y: ⊦ a ∈ x → rmdup(a ' + x) = rmdup(x);%rmdup-n: ⊦ ¬ a ∈ x → rmdup(a ' + x) = a + rmdup(x);%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ a + x = a ' + x; (s)% ⊦ x = y + x ↔ y = []; (s)% ⊦ a ' ≠ []; (s)% ⊦ a ∈ y → a ∈ x + y; (s) Used formulas: a ∈ (a0 ' + x0) + y