Theorems · Theorem · field theory
ArchimedeanClass.lt_of_stdPart_lt
∀ {K : Type u_1} [inst : LinearOrder K] [inst_1 : Field K] [inst_2 : IsOrderedRing K] {x : K} (f : ℝ →+*o K) {r : ℝ},
0 ≤ ArchimedeanClass.mk x → ArchimedeanClass.stdPart x < r → x < f r- Defined in
- Mathlib.Algebra.Order.Ring.StandardPart
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement and proof · cited by 25,697
- LinearOrderstatement and proof · cited by 8,572
- Fieldstatement and proof · cited by 7,404
- IsOrderedRingstatement and proof · cited by 777
- map_negproof · cited by 378
- ArchimedeanClassstatement · cited by 247
- ArchimedeanClass.mkstatement and proof · cited by 174
- OrderRingHomstatement and proof · cited by 132
- ArchimedeanClass.stdPartstatement and proof · cited by 42
- neg_lt_neg_iffproof · cited by 39
- ArchimedeanClass.mk_negproof · cited by 15
Cited by2
Results whose statement or proof uses this declaration.
- Hyperreal.isSt_iffproof · cited by 3
- ArchimedeanClass.le_stdPart_of_leproof · cited by 1