Theorems · Theorem · order theory
ArchimedeanClass.mk_eq_top_iff
∀ {M : Type u_1} [inst : AddCommGroup M] [inst_1 : LinearOrder M] [inst_2 : IsOrderedAddMonoid M] {a : M},
ArchimedeanClass.mk a = ⊤ ↔ a = 0- Defined in
- Mathlib.Algebra.Order.Archimedean.Class
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Top.topstatement and proof · cited by 9,680
- LinearOrderstatement and proof · cited by 8,572
- absproof · cited by 1,814
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- ArchimedeanClassstatement · cited by 247
- ArchimedeanClass.mkstatement and proof · cited by 174
- abs_zeroproof · cited by 88
- nsmul_zeroproof · cited by 73
- ArchimedeanClass.mk_eq_mkproof · cited by 8
- abs_nonpos_iffproof · cited by 3
Cited by7
Results whose statement or proof uses this declaration.
- FiniteArchimedeanClass.mem_addSubgroup_iffproof · cited by 2
- FiniteArchimedeanClass.withTopOrderIso_symm_applyproof · cited by 1
- ArchimedeanClass.out_topproof · cited by 0
- FiniteArchimedeanClass.indproof · cited by 0
- FiniteArchimedeanClass.addSubgroup_eq_botproof · cited by 0
- ArchimedeanClass.top_eq_mk_iffproof · cited by 0
- ArchimedeanClass.closedBallAddSubgroup_topproof · cited by 0