Theorems · Theorem · order theory
ArchimedeanClass.isAddRegular_mk
∀ {R : Type u_1} [inst : LinearOrder R] [inst_1 : CommRing R] [inst_2 : IsStrictOrderedRing R] {x : R},
x ≠ 0 → IsAddRegular (ArchimedeanClass.mk x)- Defined in
- Mathlib.Algebra.Order.Ring.Archimedean
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- LinearOrderstatement and proof · cited by 8,572
- IsStrictOrderedRingstatement and proof · cited by 2,490
- absproof · cited by 1,814
- nsmul_eq_mulproof · cited by 369
- ArchimedeanClassstatement and proof · cited by 247
- mul_left_commproof · cited by 184
- ArchimedeanClass.mkstatement and proof · cited by 174
- abs_mulproof · cited by 98
- abs_posproof · cited by 45
- IsAddRegularstatement · cited by 43
- ArchimedeanClass.indproof · cited by 3
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