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Proof step 17 from proof rmdup-del1-del (previous step)

a0 ∈ x0, ∀ a. rmdup(x0) -1l a = rmdup(x0 -l a) ⊦ a = a0, rmdup(x0) -1l a = (a0 ∈ x0 -l a ⊃ rmdup(x0 -l a);a0 ' + rmdup(x0 -l a))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
a0 ∈ x0, ∀ a. rmdup(x0) -1l a = rmdup(x0 -l a) ⊦ a = a0, rmdup(x0) -1l a = rmdup(x0 -l a)

Rule argument

Additional information

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