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Proof step 3 from proof ocs-del1 (previous step)

a ∈ x ⊦ #oc(a, x) = 1, a ∈ x -1l a

User applied rule structural induction

And obtained the following new goals

Proof step 4:
a ∈ a0 + x0, ∀ a. a ∈ x0 → #oc(a, x0) = 1 ∨ a ∈ x0 -1l a ⊦ #oc(a, a0 + x0) = 1, a ∈ (a0 + x0) -1l a

Rule argument

indvar: x

Additional information

Used simplifier rules: oc-e: ⊦ #oc(a, []) = 0;%list freely generated by [], +;;% ⊦ ¬ a ∈ []; (s)