Theorems · Theorem · order theory
Set.image_subtype_val_Ico
∀ {α : Type u_1} [inst : Preorder α] {s : Set α} [s.OrdConnected] (x y : ↑s), Subtype.val '' Set.Ico x y = Set.Ico ↑x ↑y- Defined in
- Mathlib.Order.Interval.Set.OrdConnected
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderSet.OrdConnected
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.Elemstatement and proof · cited by 7,166
- Set.imagestatement · cited by 5,609
- Set.Icostatement · cited by 799
- Subtype.range_coe_subtypeproof · cited by 170
- Set.OrdConnectedstatement and proof · cited by 161
- OrderEmbedding.subtypeproof · cited by 15
- OrderEmbedding.image_Icoproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- segment_image_Icoproof · cited by 1
- NNReal.image_coe_Icoproof · cited by 0
- unitInterval.volume_Icoproof · cited by 0