Theorems · Theorem · order theory
Set.IccExtend_of_right_le
∀ {α : Type u_1} {β : Type u_2} [inst : LinearOrder α] {a b : α} (h : a ≤ b) {x : α} (f : ↑(Set.Icc a b) → β),
b ≤ x → Set.IccExtend h f x = f ⟨b, ⋯⟩- Defined in
- Mathlib.Order.Interval.Set.ProjIcc
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Quot.sound
- Assumes
- LinearOrder
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
- LinearOrderstatement and proof · cited by 8,572
- Set.Elemstatement and proof · cited by 7,166
- Set.Iccstatement and proof · cited by 1,702
- Set.right_mem_Iccstatement · cited by 60
- Set.IccExtendstatement · cited by 26
- Set.projIcc_of_right_leproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- Set.IccExtend_eq_selfproof · cited by 1
- Set.IccExtend_rightproof · cited by 1
- Path.extend_of_one_leproof · cited by 0
- ContinuousMap.Homotopy.extend_apply_of_one_leproof · cited by 0