Let X and Tx be given.
Assume HTx: topology_on X Tx.
Assume Hex: ∃m : set, m ∈ ω ∧ ∀A : set, open_cover_of X Tx A → ∃B : set, open_cover_of X Tx B ∧ refines_cover B A ∧ collection_has_order_at_most_m_plus_one X B m.
We will prove finite_dimensional_space X Tx.
An exact proof term for the current goal is (andI (topology_on X Tx) (∃m : set, m ∈ ω ∧ ∀A : set, open_cover_of X Tx A → ∃B : set, open_cover_of X Tx B ∧ refines_cover B A ∧ collection_has_order_at_most_m_plus_one X B m) HTx Hex).
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