Theorems · Theorem · order theory
RingPreordering.isOrdering_iff
∀ {R : Type u_1} [inst : CommRing R] {P : RingPreordering R}, P.IsOrdering ↔ ∀ (a b : R), -(a * b) ∈ P → a ∈ P ∨ b ∈ P- Cited by
- 0 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- neg_negproof · cited by 960
- neg_mulproof · cited by 654
- mul_negproof · cited by 590
- MulMemClass.mul_memproof · cited by 173
- RingPreorderingstatement and proof · cited by 49
- Ideal.IsPrime.mem_or_memproof · cited by 22
- RingPreordering.supportproof · cited by 9
- HasMemOrNegMemproof · cited by 5
- RingPreordering.IsOrderingstatement and proof · cited by 2
- HasMemOrNegMem.neg_mem_of_notMemproof · cited by 1
- RingPreordering.IsOrdering.mk'proof · cited by 1
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