Theorems · Theorem · order theory
ArchimedeanClass.mk_le_mk_add_of_archimedean
∀ {R : Type u_1} [inst : LinearOrder R] [inst_1 : CommRing R] [inst_2 : IsStrictOrderedRing R] {S : Type u_3}
[inst_3 : LinearOrder S] [inst_4 : CommRing S] [IsStrictOrderedRing S] [Archimedean S] (f : S →+*o R) (x : R) (y : S),
ArchimedeanClass.mk x ≤ ArchimedeanClass.mk (f y) + ArchimedeanClass.mk x- Defined in
- Mathlib.Algebra.Order.Ring.Archimedean
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- LinearOrderstatement and proof · cited by 8,572
- IsStrictOrderedRingstatement and proof · cited by 2,490
- zero_addproof · cited by 2,366
- le_reflproof · cited by 2,061
- map_zeroproof · cited by 1,614
- eq_or_neproof · cited by 1,117
- Archimedeanstatement and proof · cited by 603
- ArchimedeanClassstatement and proof · cited by 247
- ArchimedeanClass.mkstatement and proof · cited by 174
- OrderRingHomstatement and proof · cited by 132
Cited by2
Results whose statement or proof uses this declaration.
- ArchimedeanClass.mk_map_nonneg_of_archimedeanproof · cited by 6
- ArchimedeanClass.mk_le_add_mk_of_archimedeanproof · cited by 0