Theorems · Theorem · order theory
Set.abs_sub_le_of_uIcc_subset_uIcc
∀ {α : Type u_1} [inst : AddCommGroup α] [inst_1 : LinearOrder α] [IsOrderedAddMonoid α] {a b c d : α},
Set.uIcc c d ⊆ Set.uIcc a b → |d - c| ≤ |b - a|If [c, d] is a subinterval of [a, b], then the distance between c and d is less than or
equal to that of a and b
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- absstatement and proof · cited by 1,814
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- Set.uIccstatement and proof · cited by 393
- sub_le_subproof · cited by 24
- max_sub_min_eq_absproof · cited by 10
- Set.uIcc_subset_uIcc_iff_leproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Set.abs_sub_left_of_mem_uIccproof · cited by 2
- Real.dist_le_of_mem_uIccproof · cited by 2
- Set.abs_sub_right_of_mem_uIccproof · cited by 1