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Proof step 2 from proof del-del1-nodups (previous step)

⊦ x -l a = x -1l a, dups(x)

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ a. x0 -l a = x0 -1l a ∨ dups(x0) ⊦ (a0 + x0) -l a = (a0 + x0) -1l a, dups(a0 + x0)

Rule argument

term: x

Additional information

Used simplifier rules: del-e: ⊦ [] -l a = [];%del1-e: ⊦ [] -1l a = [];%list freely generated by [], +;;