We will prove ∃B : set, basis_on (setprod R R) B ∧ generated_topology (setprod R R) B = R2_dictionary_order_topology.

We use (basis_of_subbasis (setprod R R) (open_rays_subbasis (setprod R R))) to witness the existential quantifier.

Apply andI to the current goal.

An exact proof term for the current goal is (finite_intersections_basis_of_subbasis (setprod R R) (open_rays_subbasis (setprod R R)) (open_rays_subbasis_is_subbasis (setprod R R))).

Use reflexivity.

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