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Proof step 5 from proof mklist-rmdup (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
∀ n, a. n = 0 ∨ rmdup(x0 + mklist(a, n)) = rmdup(x0) + a ' ∨ a ∈ x0 ⊦ a = a0, n = 0, rmdup((a0 ' + x0) + mklist(a, n)) = rmdup(a0 ' + x0) + a ', a ∈ x0

Rule argument

Additional information

Used simplifier rules: ⊦ a ∈ b ' + x ↔ ¬(a ≠ b ∧ ¬ a ∈ x); (ss)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ a + x = a ' + x; (s)