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Theorems · Theorem · order theory

strictMono_domRestrict

∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] {f : α → β} {s : Set α},
  StrictMono (s.domRestrict f) ↔ StrictMonoOn f s
Defined in
Mathlib.Data.Set.Monotone
Cited by
5 results in Mathlib
Foundations
Depth 11 from the axioms · uses propext, Quot.sound
Assumes
PreorderPreorder
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

StrictMono.of_domRestrict · cited by 4StrictMono.of_domRestrictContinuous.strictMonoOn_of_inj_rigidity · cited by 1Continuous.strictMonoOn_o…StrictMonoOn.domRestrict · cited by 1StrictMonoOn.domRestrictContinuousOn.strictMonoOn_of_injOn_Ioo · cited by 0ContinuousOn.strictMonoOn…strictMono_restrict · cited by 0strictMono_restrictSet · cited by 53352SetPreorder · cited by 7952PreorderSet.Elem · cited by 7166Set.ElemStrictMono · cited by 706StrictMonoSet.domRestrict · cited by 383Set.domRestrictStrictMonoOn · cited by 194StrictMonoOnstrictMono_domRestrictCITED BYCITES

Cites6

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Cited by5

Results whose statement or proof uses this declaration.