Theorems · Theorem · commutative algebra
RingCon.coe_sInf
∀ {R : Type u_3} [inst : Add R] [inst_1 : Mul R] (S : Set (RingCon R)), ⇑(sInf S) = sInf (DFunLike.coe '' S)The infimum of a set of congruence relations is the same as the infimum of the set's image under the map to the underlying binary relation.
- Defined in
- Mathlib.RingTheory.Congruence.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Set.imagestatement · cited by 5,609
- iInfproof · cited by 1,690
- InfSet.sInfstatement and proof · cited by 935
- RingConstatement and proof · cited by 219
- sInf_imageproof · cited by 25
- iInf_applyproof · cited by 15
- iInf_Prop_eqproof · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- RingCon.coe_iInfproof · cited by 0