Theorems · Definition · order theory
Archimedean.embedReal
(M : Type u_1) →
[inst : AddCommGroup M] →
[inst_1 : LinearOrder M] →
[IsOrderedAddMonoid M] → [inst_3 : One M] → [ZeroLEOneClass M] → [NeZero 1] → [Archimedean M] → M →+o ℝThe bundled M →+o ℝ for archimedean M that preserves 1.
- Defined in
- Mathlib.Data.Real.Embedding
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- Archimedeanstatement and proof · cited by 603
- ZeroLEOneClassstatement and proof · cited by 304
- OrderAddMonoidHomstatement · cited by 80
- Archimedean.embedRealFunproof · cited by 4
- Archimedean.embedRealFun_addproof · cited by 1
- Archimedean.embedRealFun_zeroproof · cited by 0
Cited by4
Results whose statement or proof uses this declaration.
- Archimedean.embedReal_applystatement and proof · cited by 1
- Archimedean.embedReal_injectivestatement · cited by 1
- Archimedean.exists_orderAddMonoidHom_real_injectiveproof · cited by 1
- Archimedean.embedReal_onestatement · cited by 0