Theorems · Theorem · order theory
Set.image_subtype_val_Ici_Ioi
∀ {α : Type u_1} [inst : Preorder α] {a : α} (b : ↑(Set.Ici a)), Subtype.val '' Set.Ioi b = Set.Ioi ↑b- Defined in
- Mathlib.Order.Interval.Set.Image
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
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 · 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.Ioistatement and proof · cited by 1,463
- Set.Icistatement and proof · cited by 1,070
- Set.inter_eq_rightproof · cited by 41
- Subtype.image_preimage_valproof · cited by 17
- Set.Ioi_subset_Iciproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- Set.image_subtype_val_Iic_Iioproof · cited by 1
- NNReal.image_coe_Ioiproof · cited by 1