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Proof step 9 from proof mklist-rmdup (previous step)

∀ 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

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Proof step 10:
∀ n, a. n = 0 ∨ rmdup(x0 + mklist(a, n)) = rmdup(x0) + a ' ∨ a ∈ x0, a0 ∈ x0 ∨ a0 ∈ mklist(a, n) ⊦ a = a0, n = 0, rmdup(x0 + mklist(a, n)) = rmdup(a0 ' + x0) + a ', a ∈ x0
Proof step 12:
∀ 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)

Rule argument

pos: right 1

Proof step 9 from proof mklist-rmdup (previous step)

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Rule argument

Additional information