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Theorems · Theorem · order theory

Set.IccExtend_of_mem

∀ {α : Type u_1} {β : Type u_2} [inst : LinearOrder α] {a b : α} (h : a ≤ b) {x : α} (f : ↑(Set.Icc a b) → β)
  (hx : x ∈ Set.Icc a b), Set.IccExtend h f x = f ⟨x, hx⟩
Defined in
Mathlib.Order.Interval.Set.ProjIcc
Cited by
5 results in Mathlib
Foundations
Depth 20 from the axioms · uses propext
Assumes
LinearOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Path.extend_apply · cited by 9Path.extend_applyContinuousMap.Homotopy.extend_of_mem_I · cited by 4Homotopy.extend_of_mem_IReal.sin_arcsin' · cited by 3Real.sin_arcsin'ContinuousMap.Homotopy.trans_apply · cited by 3Homotopy.trans_applyPath.range_reparam · cited by 0Path.range_reparamSet · cited by 53352SetLinearOrder · cited by 8572LinearOrderSet.Elem · cited by 7166Set.ElemSet.Icc · cited by 1702Set.IccSet.IccExtend · cited by 26Set.IccExtendSet.projIcc_of_mem · cited by 11Set.projIcc_of_memSet.IccExtend_of_memCITED BYCITES

Cites6

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

Cited by5

Results whose statement or proof uses this declaration.