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Theorems · Theorem · order theory

StrictMono.of_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

Alias of the forward direction of strictMono_domRestrict.

Defined in
Mathlib.Data.Set.Monotone
Cited by
4 results in Mathlib
Foundations
Depth 12 from the axioms · uses propext, Quot.sound
Assumes
PreorderPreorder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

ContinuousOn.strictMonoOn_of_injOn_Icc · cited by 2ContinuousOn.strictMonoOn…sup_strictMonoOn_Icc_inf · cited by 0sup_strictMonoOn_Icc_infStrictMono.of_restrict · cited by 0StrictMono.of_restrictinf_strictMonoOn_Icc_sup · cited by 0inf_strictMonoOn_Icc_supSet · cited by 53352SetPreorder · cited by 7952PreorderSet.Elem · cited by 7166Set.ElemStrictMono · cited by 706StrictMonoSet.domRestrict · cited by 383Set.domRestrictStrictMonoOn · cited by 194StrictMonoOnstrictMono_domRestrict · cited by 5strictMono_domRestrictStrictMono.of_domRestrictCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by4

Results whose statement or proof uses this declaration.