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Proof step 4 from proof rmdup-last (previous step)

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

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 5:
a0 ∈ x0, ∀ a. rmdup(x0 + a ') = rmdup(x0) + a ' ∨ a ∈ x0 ⊦ rmdup((a0 ' + x0) + a ') = rmdup(a0 ' + x0) + a ', a = a0, a ∈ x0
Proof step 7:
∀ a. rmdup(x0 + a ') = rmdup(x0) + a ' ∨ a ∈ x0 ⊦ a0 ∈ x0, rmdup((a0 ' + x0) + a ') = rmdup(a0 ' + x0) + a ', a = a0, a ∈ x0

Rule argument

fma: a0 ∈ x0

Additional information

Used formulas: a0 ∈ x0