12 lines
375 B
Plaintext
12 lines
375 B
Plaintext
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import Mathlib.Topology.DiscreteSubset
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theorem codiscreteWithin_congr
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{X : Type u_1} [TopologicalSpace X]
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{S T U : Set X}
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(hST : S ∩ U = T ∩ U) :
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S ∈ Filter.codiscreteWithin U ↔ T ∈ Filter.codiscreteWithin U := by
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repeat rw [mem_codiscreteWithin]
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rw [← Set.diff_inter_self_eq_diff (t := S)]
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rw [← Set.diff_inter_self_eq_diff (t := T)]
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rw [hST]
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