Theorems · Theorem · order theory
MulArchimedean.of_locallyFiniteOrder
∀ {G : Type u_2} [inst : CommGroup G] [inst_1 : LinearOrder G] [IsOrderedMonoid G] [LocallyFiniteOrder G],
MulArchimedean GAny locally finite linear group is mul-archimedean.
- Defined in
- Mathlib.GroupTheory.ArchimedeanDensely
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- LocallyFiniteOrderstatement and proof · cited by 658
- IsOrderedMonoidstatement and proof · cited by 577
- MulArchimedeanstatement · cited by 45
- MulArchimedean.comapproof · cited by 5
- OrderMonoidHom.toMonoidHomproof · cited by 5
- LocallyFiniteOrder.orderMonoidHomproof · cited by 4
- LocallyFiniteOrder.orderMonoidHom_strictMonoproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Valued.integer.mulArchimedean_mrange_of_isCompact_integerproof · cited by 1