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Proof step 2 from proof k-union-rec-n (previous step)

⊦ rmdup((a ' + x) + y) = a ' + rmdup(x + y), a ∈ x, a ∈ y

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: list-dup inst: name: rmdup-n seq: ⊦ ¬ a ∈ x → rmdup(a ' + x) = a + rmdup(x) subst: [x, a] → [x + y, a] flags: rewrite

Additional information

Used simplifier rules: c: ⊦ a + x = a ' + x; from specification list%app-01: ⊦ x + y = x + z ↔ y = z; from specification list%rmdup-y: ⊦ a ∈ x → rmdup(a ' + x) = rmdup(x); from specification list-dup%app-05: ⊦ x = y + x ↔ y = []; from specification list%e: ⊦ a ' ≠ []; from specification list%in-append: ⊦ a ∈ x + y ↔ ¬ ¬(a ∈ x ∨ a ∈ y); from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: x + y, a