Theorems · Theorem · order theory
MulArchimedeanClass.mk_lt_mk
∀ {M : Type u_1} [inst : CommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedMonoid M] {a b : M},
MulArchimedeanClass.mk a < MulArchimedeanClass.mk b ↔ ∀ (n : ℕ), |b|ₘ ^ n < |a|ₘ- 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.
- LinearOrderstatement and proof · cited by 8,572
- CommGroupstatement and proof · cited by 990
- IsOrderedMonoidstatement and proof · cited by 577
- mabsstatement · cited by 148
- MulArchimedeanClassstatement · cited by 81
- MulArchimedeanClass.mkstatement · cited by 63
Cited by6
Results whose statement or proof uses this declaration.
- MulArchimedeanClass.min_le_mk_mulproof · cited by 4
- MulArchimedeanClass.mk_mul_eq_mk_leftproof · cited by 3
- MulArchimedeanClass.mk_antitoneOnproof · cited by 1
- MulArchimedeanClass.lt_of_mk_lt_mk_of_le_oneproof · cited by 1
- MulArchimedeanClass.lt_of_mk_lt_mk_of_one_leproof · cited by 0
- MulArchimedeanClass.mk_monotoneOnproof · cited by 0