Theorems · Theorem · convex and discrete geometry
Ioo_subset_openSegment
∀ {𝕜 : Type u_1} [inst : Field 𝕜] [inst_1 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜] {x y : 𝕜},
Set.Ioo x y ⊆ openSegment 𝕜 x y- Defined in
- Mathlib.Analysis.Convex.Segment
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- Fieldstatement and proof · cited by 7,404
- IsStrictOrderedRingstatement and proof · cited by 2,490
- LT.lt.ne'proof · cited by 1,417
- Set.Ioostatement and proof · cited by 1,214
- LT.lt.neproof · cited by 872
- openSegmentstatement · cited by 102
- Set.Ioo_subset_Icc_selfproof · cited by 54
- Icc_subset_segmentproof · cited by 3
- mem_openSegment_of_ne_left_rightproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- openSegment_eq_Iooproof · cited by 4
- Convex.Ioo_subset_of_mem_closureproof · cited by 3
- Convex.interior_closure_eq_interior_of_nonempty_interiorproof · cited by 1
- ConvexOn.le_right_of_left_le''proof · cited by 1
- ConvexOn.le_left_of_right_le''proof · cited by 1