Theorems · Theorem · order theory
add_lt_add_of_lt_of_le
∀ {α : Type u_1} [inst : Add α] [inst_1 : Preorder α] [AddLeftMono α] [AddRightStrictMono α] {a b c d : α},
a < b → c ≤ d → a + c < b + d- Cited by
- 37 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
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.
- Preorderstatement and proof · cited by 7,952
- LE.le.trans_ltproof · cited by 795
- AddLeftMonostatement and proof · cited by 687
- AddRightStrictMonostatement and proof · cited by 160
- add_lt_add_leftproof · cited by 47
- add_le_add_rightproof · cited by 37
Cited by37
Results whose statement or proof uses this declaration.
- convex_Iioproof · cited by 6
- StrictConvexOn.add_convexOnproof · cited by 5
- Hyperreal.infinitePos_add_not_infiniteNegproof · cited by 4
- ConvexOn.le_left_of_right_le'proof · cited by 3
- le_or_lt_of_add_le_addproof · cited by 3
- ConvexOn.convex_ltproof · cited by 3
- Metric.ball_subsetproof · cited by 3
- hasSum_ltproof · cited by 3
- Multiset.disjSum_lt_disjSum_of_lt_of_leproof · cited by 2
- PadicInt.appr_ltproof · cited by 2
- ConvexOn.lipschitzOnWith_of_abs_leproof · cited by 2
- List.sum_lt_sumproof · cited by 2