Theorems · Theorem · order theory
add_lt_add_of_lt_of_lt
∀ {α : Type u_1} [inst : Add α] [inst_1 : Preorder α] [AddLeftStrictMono α] [AddRightStrictMono α] {a b c d : α},
a < b → c < d → a + c < b + d- Cited by
- 13 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- AddLeftStrictMonostatement and proof · cited by 203
- AddRightStrictMonostatement and proof · cited by 160
- add_lt_add_rightproof · cited by 50
- add_lt_add_leftproof · cited by 47
Cited by13
Results whose statement or proof uses this declaration.
- add_lt_addproof · cited by 35
- trichotomy_of_add_eq_addproof · cited by 3
- isCompact_setOfPred_finiteMeasure_mass_le_compl_isCompact_leproof · cited by 2
- Delone.DeloneSet.eq_of_mem_ballproof · cited by 1
- cauchy_productproof · cited by 1
- sub_le_neg_add_iffproof · cited by 1
- StrictAnti.addproof · cited by 1
- StrictMonoOn.addproof · cited by 0
- le_or_le_of_add_le_addproof · cited by 0
- StrictMono.addproof · cited by 0
- StrictAntiOn.addproof · cited by 0
- sub_lt_subproof · cited by 0