Theorems · Theorem · order theory
Set.projIcc_of_mem
∀ {α : Type u_1} [inst : LinearOrder α] {a b : α} (h : a ≤ b) {x : α} (hx : x ∈ Set.Icc a b),
Set.projIcc a b h x = ⟨x, hx⟩- Defined in
- Mathlib.Order.Interval.Set.ProjIcc
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext
- 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 · cited by 7,166
- Set.Iccstatement and proof · cited by 1,702
- sup_of_le_rightproof · cited by 143
- inf_of_le_rightproof · cited by 128
- Set.projIccstatement · cited by 56
Cited by11
Results whose statement or proof uses this declaration.
- Set.projIcc_valproof · cited by 14
- Set.IccExtend_of_memproof · cited by 5
- Manifold.riemannianEDist_le_pathELengthproof · cited by 4
- ODE.FunSpace.compProj_of_memproof · cited by 3
- eVariationOn.sum_le_of_monotoneOn_Iccproof · cited by 2
- unitInterval.qRight_zero_rightproof · cited by 1
- mfderivWithin_projIcc_oneproof · cited by 1
- Set.strictMonoOn_projIccproof · cited by 1
- mfderiv_subtypeVal_Icc_oneproof · cited by 1
- mfderivWithin_comp_projIcc_oneproof · cited by 1
- IsPicardLindelof.exists_eq_forall_mem_Icc_eq_picardproof · cited by 0