Theorems · Theorem · commutative algebra
Ring.HasFiniteQuotients.finite_setOfPred_mem
∀ {R : Type u_1} [inst : CommRing R] [Ring.HasFiniteQuotients R] (x : R), x ≠ 0 → {I | x ∈ I}.Finite- Cited by
- 2 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- Set.ofPredstatement and proof · cited by 6,101
- Idealstatement and proof · cited by 4,748
- Bot.botproof · cited by 4,720
- Finiteproof · cited by 3,029
- HasQuotient.Quotientproof · cited by 2,301
- Set.Finitestatement and proof · cited by 1,814
- Ideal.spanproof · cited by 948
- Ideal.Quotient.mkproof · cited by 610
- Ideal.comapproof · cited by 443
- Ideal.Quotient.mk_surjectiveproof · cited by 134
- RelIso.toEquivproof · cited by 113
Cited by2
Results whose statement or proof uses this declaration.
- Ring.HasFiniteQuotients.finite_cardQuot_leproof · cited by 2
- Ring.HasFiniteQuotients.finite_setOf_memproof · cited by 0