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Proof step 15 from proof del-rmdup (previous step)

∀ a. rmdup(x0 -l a) = rmdup(x0) -l a ⊦ a = a0, (a0 ∈ x0 -l a ⊃ rmdup(x0 -l a);a0 ' + rmdup(x0 -l a)) = rmdup(a0 ' + x0) -l a

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
∀ a. rmdup(x0 -l a) = rmdup(x0) -l a ⊦ a = a0, (a0 ∈ x0 ⊃ rmdup(x0 -l a);a0 ' + rmdup(x0 -l a)) = rmdup(a0 ' + x0) -l a

Rule argument

Additional information

Used simplifier rules: in-del-new: ⊦ a ∈ x -l b ↔ a ∈ x ∧ a ≠ b;