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Proof step 6 from proof mklist-rmdup (previous step)

∀ a, n. rmdup(x0 + mklist(a, n)) = rmdup(x0) + a ' ∨ n = 0 ∨ a ∈ x0 ⊦ n = 0, (a0 ∈ x0 + mklist(a, n) ⊃ rmdup(x0 + mklist(a, n));a0 ' + rmdup(x0 + mklist(a, n))) = rmdup(a0 ' + x0) + a ', a = a0, a ∈ x0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
∀ a, n. rmdup(x0 + mklist(a, n)) = rmdup(x0) + a ' ∨ n = 0 ∨ a ∈ x0 ⊦ a = a0, n = 0, (a0 ∈ x0 ∨ a0 ∈ mklist(a, n) ⊃ rmdup(x0 + mklist(a, n));a0 ' + rmdup(x0 + mklist(a, n))) = rmdup(a0 ' + x0) + a ', a ∈ x0

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list%in-append: ⊦ a ∈ x + y ↔ ¬ ¬(a ∈ x ∨ a ∈ y); from specification list