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theorem proved term proof

finite_resolution_mono

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formal statement (Lean)

  54theorem finite_resolution_mono {c : C} {U V : Set C}
  55    (hU : U ∈ L.N c) (hV : V ∈ L.N c) (hVU : V ⊆ U) (hfin : (r.R '' U).Finite) :
  56    (r.R '' V).Finite :=

proof body

Term-mode proof.

  57  Set.Finite.subset hfin (Set.image_mono hVU)
  58
  59/-! ## Consequences for Resolution Cells -/
  60
  61/-- If R has finite local resolution at c, the resolution cell at c
  62    has a finite number of "neighbors" in any finite-resolution neighborhood -/

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