Theorems · Inductive type · order theory
RingPreordering
(R : Type u_1) → [CommRing R] → Type u_1
A preordering on a ring R is a subsemiring of R containing all squares,
but not containing -1.
- Defined in
- Mathlib.Algebra.Order.Ring.Ordering.Defs
- Cited by
- 49 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement · cited by 17,173
Cited by66
Results whose statement or proof uses this declaration.
- RingPreordering.toSubsemiringstatement and proof · cited by 12
- RingPreordering.HasIdealSupportstatement · cited by 11
- RingPreordering.supportstatement and proof · cited by 9
- RingPreordering.supportAddSubgroupstatement and proof · cited by 7
- RingPreordering.mem_of_isSquarestatement and proof · cited by 4
- RingPreordering.copystatement and proof · cited by 3
- RingPreordering.hasIdealSupport_iffstatement and proof · cited by 3
- RingPreordering.neg_one_notMemstatement and proof · cited by 3
- RingPreordering.IsOrderingstatement · cited by 2
- RingPreordering.extstatement and proof · cited by 2
- RingPreordering.mk'statement · cited by 2
- RingPreordering.HasIdealSupport.smul_mem_supportstatement and proof · cited by 1