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Proof step 22 from proof rmdup-del1-del (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
∀ a. rmdup(x0) -1l a = rmdup(x0 -l a) ⊦ rmdup(x0) -1l a = rmdup(x0 -l a), a = a0, a0 ∈ x0

Rule argument

Additional information

Used simplifier rules: in-del-new: ⊦ a ∈ x -l b ↔ a ∈ x ∧ a ≠ b;%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ x + y = x + z ↔ y = z; (s)