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Proof step 8 from proof mklist-rmdup (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
∀ n, a. n = 0 ∨ rmdup(x0 + mklist(a, n)) = rmdup(x0) + a ' ∨ a ∈ x0 ⊦ (a0 ∈ x0 ∨ a0 ∈ mklist(a, n) ⊃ rmdup(x0 + mklist(a, n));a0 ' + rmdup(x0 + mklist(a, n))) = rmdup(a0 ' + x0) + a ', a = a0, n = 0, a ∈ x0

Rule argument

Additional information

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