Theorems · Theorem · order theory
Set.image_update_Ico_left
∀ {ι : Type u_1} {α : ι → Type u_2} [inst : DecidableEq ι] [inst_1 : (i : ι) → PartialOrder (α i)] (f : (i : ι) → α i)
(i : ι) (a : α i), Function.update f i '' Set.Ico a (f i) = Set.Ico (Function.update f i a) f- Defined in
- Mathlib.Order.Interval.Set.Pi
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqPartialOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- PartialOrderstatement and proof · cited by 6,410
- Set.imagestatement and proof · cited by 5,609
- Set.Icostatement and proof · cited by 799
- Function.updatestatement and proof · cited by 502
- Function.update_eq_selfproof · cited by 41
- Set.image_update_Icoproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- Set.image_mulSingle_Ico_leftproof · cited by 0
- Set.image_single_Ico_leftproof · cited by 0