Theorems · Theorem · order theory
ArchimedeanClass.mk_add_eq_mk_left
∀ {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 + b) = ArchimedeanClass.mk a- Defined in
- Mathlib.Algebra.Order.Archimedean.Class
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- LE.le.transproof · cited by 3,151
- LT.lt.leproof · cited by 2,189
- le_antisymmproof · cited by 2,068
- absproof · cited by 1,814
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- add_commproof · cited by 1,535
- ArchimedeanClassstatement · cited by 247
- ArchimedeanClass.mkstatement and proof · cited by 174
- two_nsmulproof · cited by 67
- add_le_add_iff_rightproof · cited by 47
Cited by4
Results whose statement or proof uses this declaration.
- ArchimedeanClass.mk_sumproof · cited by 2
- ArchimedeanClass.mk_add_eq_mk_rightproof · cited by 2
- HahnEmbedding.Partial.eval_ltproof · cited by 1
- ArchimedeanClass.mk_sub_eq_mk_leftproof · cited by 0