Theorems · Theorem · order theory
ArchimedeanClass.min_le_mk_add
∀ {M : Type u_1} [inst : AddCommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedAddMonoid M] (a b : M),
min (ArchimedeanClass.mk a) (ArchimedeanClass.mk b) ≤ ArchimedeanClass.mk (a + b)- Defined in
- Mathlib.Algebra.Order.Archimedean.Class
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- absproof · cited by 1,814
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- LT.lt.trans_leproof · cited by 678
- not_leproof · cited by 328
- ArchimedeanClassstatement · cited by 247
- ArchimedeanClass.mkstatement and proof · cited by 174
- two_nsmulproof · cited by 67
- LT.lt.not_gtproof · cited by 54
- add_lt_add_iff_rightproof · cited by 42
- add_lt_add_iff_leftproof · cited by 30
Cited by5
Results whose statement or proof uses this declaration.
- ArchimedeanClass.mk_left_le_mk_addproof · cited by 4
- ArchimedeanClass.min_le_mk_subproof · cited by 1
- ArchimedeanClass.mk_right_le_mk_addproof · cited by 1
- FiniteArchimedeanClass.min_le_mk_addproof · cited by 0
- ArchimedeanClass.FiniteElement.mk_add_mkstatement · cited by 0