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

∀ a. rmdup(x0 -l a) = rmdup(x0) -l a ⊦ a0 ∈ x0, a = a0, (a0 ∈ x0 ⊃ 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 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);%app-08: ⊦ a ' + x = a ' + y ↔ x = y; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%c: ⊦ a + x = a ' + x; from specification list%rmdup-n: ⊦ ¬ a ∈ x → rmdup(a ' + x) = a + rmdup(x); from specification list-dup