Theorems · Theorem · order theory
Set.projIcc_of_right_le
∀ {α : Type u_1} [inst : LinearOrder α] {a b : α} (h : a ≤ b) {x : α}, b ≤ x → Set.projIcc a b h x = ⟨b, ⋯⟩- Defined in
- Mathlib.Order.Interval.Set.ProjIcc
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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 · cited by 1,702
- inf_of_le_leftproof · cited by 186
- sup_of_le_rightproof · cited by 143
- Set.right_mem_Iccstatement and proof · cited by 60
- Set.projIccstatement · cited by 56
Cited by5
Results whose statement or proof uses this declaration.
- Real.arcsin_of_one_leproof · cited by 7
- Set.IccExtend_of_right_leproof · cited by 4
- Set.projIcc_rightproof · cited by 2
- unitInterval.symm_projIccproof · cited by 1
- unitInterval.qRight_one_leftproof · cited by 0