Theorems · Theorem · order theory
Archimedean.ratLt_nonempty
∀ {M : Type u_1} [inst : AddCommGroup M] [inst_1 : LinearOrder M] [IsOrderedAddMonoid M] [inst_3 : One M]
[ZeroLEOneClass M] [NeZero 1] [Archimedean M] (x : M), (Archimedean.ratLt x).Nonempty- Defined in
- Mathlib.Data.Real.Embedding
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
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
- LinearOrderstatement and proof · cited by 8,572
- Set.Nonemptystatement · cited by 2,627
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- one_smulproof · cited by 1,374
- LE.le.trans_ltproof · cited by 795
- Archimedeanstatement and proof · cited by 603
- zero_lt_oneproof · cited by 598
- lt_of_lt_of_leproof · cited by 438
- Int.cast_natCastproof · cited by 393
- Int.cast_oneproof · cited by 371
- neg_smulproof · cited by 306
Cited by1
Results whose statement or proof uses this declaration.
- Archimedean.ratLt'_nonemptyproof · cited by 3