Theorems · Theorem · order theory
Set.projIcc_val
∀ {α : Type u_1} [inst : LinearOrder α] {a b : α} (h : a ≤ b) (x : ↑(Set.Icc a b)), Set.projIcc a b h ↑x = x- Defined in
- Mathlib.Order.Interval.Set.ProjIcc
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 20 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.projIccstatement · cited by 56
- Set.projIcc_of_memproof · cited by 11
Cited by14
Results whose statement or proof uses this declaration.
- Set.IccExtend_valproof · cited by 5
- ContinuousMap.concat_comp_IccInclusionLeftproof · cited by 2
- Manifold.lintegral_norm_mfderiv_Icc_eq_pathELength_projIccproof · cited by 2
- contMDiffOn_comp_projIcc_iffproof · cited by 2
- ODE.FunSpace.compProj_valproof · cited by 2
- Set.projIcc_surjectiveproof · cited by 2
- unitInterval.qRight_one_rightproof · cited by 1
- unitInterval.symm_projIccproof · cited by 1
- isQuotientMap_projIccproof · cited by 1
- mdifferentiableWithinAt_comp_projIcc_iffproof · cited by 1
- mfderivWithin_comp_projIcc_oneproof · cited by 1
- contMDiffWithinAt_comp_projIcc_iffproof · cited by 0