Theorems · Theorem · order theory
ArchimedeanClass.mk_lt_mk
∀ {M : Type u_1} [inst : AddCommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedAddMonoid M] {a b : M},
ArchimedeanClass.mk a < ArchimedeanClass.mk b ↔ ∀ (n : ℕ), n • |b| < |a|- Defined in
- Mathlib.Algebra.Order.Archimedean.Class
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- absstatement · cited by 1,814
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- ArchimedeanClassstatement · cited by 247
- ArchimedeanClass.mkstatement · cited by 174
Cited by6
Results whose statement or proof uses this declaration.
- ArchimedeanClass.lt_of_mk_lt_mk_of_nonposproof · cited by 6
- ArchimedeanClass.lt_of_mk_lt_mk_of_nonnegproof · cited by 5
- ArchimedeanClass.min_le_mk_addproof · cited by 5
- ArchimedeanClass.mk_add_eq_mk_leftproof · cited by 4
- ArchimedeanClass.mk_antitoneOnproof · cited by 1
- ArchimedeanClass.mk_monotoneOnproof · cited by 0