Theorems · Theorem · order theory
Archimedean.ratLt_add
∀ {M : Type u_1} [inst : AddCommGroup M] [inst_1 : LinearOrder M] [IsOrderedAddMonoid M] [inst_3 : One M]
[ZeroLEOneClass M] [NeZero 1] [Archimedean M] (x y : M),
Archimedean.ratLt (x + y) = Archimedean.ratLt x + Archimedean.ratLt y- Defined in
- Mathlib.Data.Real.Embedding
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites37
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- LE.le.transproof · cited by 3,151
- zero_addproof · cited by 2,366
- Set.extproof · cited by 2,266
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- Set.Icoproof · cited by 799
- Archimedeanstatement and proof · cited by 603
- zero_lt_oneproof · cited by 598
- lt_of_lt_of_leproof · cited by 438
- smul_smulproof · cited by 360
Cited by1
Results whose statement or proof uses this declaration.
- Archimedean.ratLt'_addproof · cited by 1