Theorems · Theorem · order theory
MulArchimedeanClass.mk_eq_top_iff
∀ {M : Type u_1} [inst : CommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedMonoid M] {a : M},
MulArchimedeanClass.mk a = ⊤ ↔ a = 1- Defined in
- Mathlib.Algebra.Order.Archimedean.Class
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 34 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.
- Top.topstatement and proof · cited by 9,680
- LinearOrderstatement and proof · cited by 8,572
- CommGroupstatement and proof · cited by 990
- IsOrderedMonoidstatement and proof · cited by 577
- one_powproof · cited by 521
- mabsproof · cited by 148
- MulArchimedeanClassstatement · cited by 81
- MulArchimedeanClass.mkstatement and proof · cited by 63
- mabs_oneproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- FiniteMulArchimedeanClass.withTopOrderIso_symm_applyproof · cited by 0
- MulArchimedeanClass.out_topproof · cited by 0
- MulArchimedeanClass.top_eq_mk_iffproof · cited by 0