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Proof step 10 from proof mklist-rmdup (previous step)

¬(a0 ∈ x0 ∨ a0 ∈ mklist(a, n)), ∀ a, n. rmdup(x0 + mklist(a, n)) = rmdup(x0) + a ' ∨ n = 0 ∨ a ∈ x0 ⊦ 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 11:
∀ a, n. rmdup(x0 + mklist(a, n)) = rmdup(x0) + a ' ∨ n = 0 ∨ a ∈ x0 ⊦ a = a0, n = 0, rmdup(x0 + mklist(a, n)) = rmdup(x0) + a ', a ∈ x0, a0 ∈ x0, a0 ∈ mklist(a, n)

Rule argument

Additional information

Used simplifier rules: app-08: ⊦ a ' + x = a ' + y ↔ x = y; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%c: ⊦ a + x = a ' + x; from specification list%rmdup-n: ⊦ ¬ a ∈ x → rmdup(a ' + x) = a + rmdup(x); from specification list-dup