Theorems · Theorem · order theory
add_lt_add_of_le_of_lt
∀ {α : Type u_1} [inst : Add α] [inst_1 : Preorder α] [AddLeftStrictMono α] [AddRightMono α] {a b c d : α},
a ≤ b → c < d → a + c < b + d- Cited by
- 31 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
- AddRightMonostatement and proof · cited by 367
- AddLeftStrictMonostatement and proof · cited by 203
- add_lt_add_rightproof · cited by 50
- add_le_add_leftproof · cited by 37
Cited by31
Results whose statement or proof uses this declaration.
- Ordinal.isPrincipal_add_omega0_opowproof · cited by 7
- MonovaryOn.sum_smul_comp_perm_eq_sum_smul_iffproof · cited by 5
- IsCauSeq.boundedproof · cited by 3
- tendsto_integral_exp_inner_smul_cocompactproof · cited by 3
- ConvexOn.lt_left_of_right_lt'proof · cited by 3
- Metric.closedBall_disjoint_ballproof · cited by 2
- ContinuousMap.idealOfSet_ofIdeal_eq_closureproof · cited by 2
- Metric.dist_lt_add_of_nonempty_closedBall_inter_ballproof · cited by 2
- add_le_add_iff_of_geproof · cited by 2
- List.sum_lt_sumproof · cited by 2
- Multiset.disjSum_lt_disjSum_of_le_of_ltproof · cited by 2
- bernsteinApproximation_uniformproof · cited by 1