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Proof step 12 from proof mklist-rmdup (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
∀ n, a. n = 0 ∨ rmdup(x0 + mklist(a, n)) = rmdup(x0) + a ' ∨ a ∈ x0 ⊦ a = a0, n = 0, rmdup(x0 + mklist(a, n)) = rmdup(x0) + a ', a0 ∈ mklist(a, n), a0 ∈ x0, a ∈ x0

Rule argument

Additional information

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