Theorems · Theorem · order theory
ArchimedeanClass.mk_left_le_mk_add
∀ {M : Type u_1} [inst : AddCommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedAddMonoid M] {a b : M},
ArchimedeanClass.mk a ≤ ArchimedeanClass.mk b → ArchimedeanClass.mk a ≤ ArchimedeanClass.mk (a + b)- Defined in
- Mathlib.Algebra.Order.Archimedean.Class
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- ArchimedeanClassstatement · cited by 247
- inf_of_le_leftproof · cited by 186
- ArchimedeanClass.mkstatement and proof · cited by 174
- ArchimedeanClass.min_le_mk_addproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- ArchimedeanClass.mk_add_eq_mk_leftproof · cited by 4
- ArchimedeanClass.mk_left_le_mk_add_iffproof · cited by 2
- ArchimedeanClass.mk_left_le_mk_subproof · cited by 2
- HahnEmbedding.Partial.archimedeanClassMk_le_of_eval_eqproof · cited by 1