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

∀ a, y. a ∈ x0 → rmdup(a ' + x0 + y) = rmdup(x0 + y), a = a0 ∨ a ∈ x0 ⊦ 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%c: ⊦ a + x = a ' + x; from specification list%app-05: ⊦ x = y + x ↔ y = []; from specification list%e: ⊦ a ' ≠ []; from specification list%in-06: ⊦ ¬ a ∈ b ' + x ↔ a ≠ b ∧ ¬ a ∈ x; from specification list%in-append: ⊦ a ∈ x + y ↔ ¬ ¬(a ∈ x ∨ a ∈ y); from specification list Used formulas: a ∈ (a0 ' + x0) + y