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Proof step 19 from proof del-rmdup (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
∀ a. rmdup(x0 -l a) = rmdup(x0) -l a ⊦ a = a0, rmdup(x0 -l a) = rmdup(x0) -l a, a0 ∈ x0

Rule argument

Additional information

Used simplifier rules: del-n: ⊦ a ≠ b → (b ' + x) -l a = b ' + (x -l a);% ⊦ x + y = x + z ↔ y = z; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ a + x = a ' + x; (s)% ⊦ ¬ a ∈ x → rmdup(a ' + x) = a + rmdup(x); (s)