Theorems · Theorem · order theory
Set.IccExtend_val
∀ {α : Type u_1} {β : Type u_2} [inst : LinearOrder α] {a b : α} (h : a ≤ b) (f : ↑(Set.Icc a b) → β)
(x : ↑(Set.Icc a b)), Set.IccExtend h f ↑x = f x- Defined in
- Mathlib.Order.Interval.Set.ProjIcc
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.IccExtendstatement · cited by 26
- Set.projIcc_valproof · cited by 14
Cited by5
Results whose statement or proof uses this declaration.
- Path.extend_extends'proof · cited by 3
- Real.arcsin_projIccproof · cited by 2
- Convex.curveIntegral_segment_add_eq_of_hasFDerivWithinAt_symmetricproof · cited by 1
- Set.IccExtend_eq_selfproof · cited by 1
- ContinuousMap.Homotopy.extend_apply_coeproof · cited by 0