Theorems · Theorem · order theory
ArchimedeanClass.min_le_mk_of_le_of_le
∀ {M : Type u_1} [inst : AddCommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedAddMonoid M] {x y z : M},
y ≤ x → x ≤ z → min (ArchimedeanClass.mk y) (ArchimedeanClass.mk z) ≤ ArchimedeanClass.mk x- Defined in
- Mathlib.Algebra.Order.Archimedean.Class
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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_reflproof · cited by 2,061
- absproof · cited by 1,814
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- le_totalproof · cited by 294
- abs_of_nonnegproof · cited by 279
- ArchimedeanClassstatement and proof · cited by 247
- ArchimedeanClass.mkstatement and proof · cited by 174
- abs_nonnegproof · cited by 168
- LE.le.trans'proof · cited by 140
- max_eq_leftproof · cited by 96
Cited by1
Results whose statement or proof uses this declaration.
- ArchimedeanClass.mk_nonneg_of_le_of_le_of_archimedeanproof · cited by 3