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Theorem sharingok-def

⊦ sharingok(lext, rext, lren, rren) ↔ (∀ la, ra. (lren(la) = rren(ra) → lext(la) ≠ None ∧ rext(ra) ≠ None ∧ lext(la) = rext(ra)) ∧ (¬ cod(rren)(lren(la)) ∧ ¬ cod(lren)(rren(ra)) ∧ lext(la) ≠ None ∧ rext(ra) ≠ None → lext(la) ≠ rext(ra)))