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Proof step 10 from proof del-rmdup (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
∀ a. rmdup(x0 -l a) = rmdup(x0) -l a ⊦ rmdup(x0) = rmdup(x0) -l a0, a0 ∈ x0

Rule argument

Additional information

Used simplifier rules: in-03: ⊦ ¬ a ∈ x → x -l a = x;%del-y: ⊦ (a ' + x) -l a = x -l a;%a: ⊦ (x + y) + z = x + y + z; from specification list