Theorems · Definition · field theory
ArchimedeanClass.FiniteElement.mk
{K : Type u_1} →
[inst : LinearOrder K] →
[inst_1 : Field K] →
[inst_2 : IsOrderedRing K] → (x : K) → 0 ≤ ArchimedeanClass.mk x → ArchimedeanClass.FiniteElement KThe constructor for FiniteElement.
- Defined in
- Mathlib.Algebra.Order.Ring.StandardPart
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Fieldstatement and proof · cited by 7,404
- IsOrderedRingstatement and proof · cited by 777
- ArchimedeanClassstatement · cited by 247
- ArchimedeanClass.mkstatement and proof · cited by 174
- ArchimedeanClass.FiniteElementstatement · cited by 36
Cited by25
Results whose statement or proof uses this declaration.
- ArchimedeanClass.stdPartproof · cited by 42
- ArchimedeanClass.FiniteResidueField.ofArchimedeanproof · cited by 7
- ArchimedeanClass.stdPart_eq_zeroproof · cited by 6
- ArchimedeanClass.stdPart_negproof · cited by 5
- ArchimedeanClass.mk_sub_pos_iffproof · cited by 2
- ArchimedeanClass.stdPart_addproof · cited by 2
- ArchimedeanClass.stdPart_invproof · cited by 2
- ArchimedeanClass.stdPart_of_mk_nonnegstatement and proof · cited by 2
- ArchimedeanClass.FiniteResidueField.ofArchimedean_applystatement · cited by 2
- ArchimedeanClass.ofArchimedean_stdPartstatement and proof · cited by 1
- ArchimedeanClass.FiniteElement.mk_le_mkstatement · cited by 1
- ArchimedeanClass.FiniteElement.mk_mul_mkstatement · cited by 1