Theorems · Theorem · order theory
Set.OrdConnected.out
∀ {α : Type u_1} [inst : Preorder α] {s : Set α}, s.OrdConnected → ∀ ⦃x : α⦄, x ∈ s → ∀ ⦃y : α⦄, y ∈ s → Set.Icc x y ⊆ s- Defined in
- Mathlib.Order.Interval.Set.OrdConnected
- Cited by
- 47 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- Set.Iccstatement · cited by 1,702
- Set.OrdConnectedstatement and proof · cited by 161
- Set.OrdConnected.out'proof · cited by 8
Cited by47
Results whose statement or proof uses this declaration.
- Set.OrdConnected.strictConvexproof · cited by 9
- Set.OrdConnected.image_hasDerivWithinAtproof · cited by 6
- Set.OrdConnected.uIcc_subsetproof · cited by 6
- ConvexOn.le_slope_of_hasDerivWithinAt_Ioiproof · cited by 5
- Set.OrdConnected.dualproof · cited by 5
- ConvexOn.slope_le_of_hasDerivWithinAt_Iioproof · cited by 5
- Set.OrdConnected.upperClosure_inter_lowerClosureproof · cited by 5
- MonotoneOn.convexOn_of_derivproof · cited by 4
- StrictConvexOn.lt_slope_of_hasDerivWithinAt_Ioiproof · cited by 4
- StrictConvexOn.slope_lt_of_hasDerivWithinAt_Iioproof · cited by 4
- Set.OrdConnected.interproof · cited by 4
- Set.OrdConnected.measurableSetproof · cited by 4