Theorems · Theorem · commutative algebra
RingCon.sSup_eq_ringConGen
∀ {R : Type u_3} [inst : Add R] [inst_1 : Mul R] (S : Set (RingCon R)), sSup S = ringConGen fun x y => ∃ c ∈ S, c x yThe supremum of a set of congruence relations S equals the smallest congruence relation
containing the binary relation 'there exists c ∈ S such that x is related to y by c'.
- Defined in
- Mathlib.RingTheory.Congruence.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
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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.imageproof · cited by 5,609
- SupSet.sSupstatement and proof · cited by 954
- RingConstatement and proof · cited by 219
- iSup_applyproof · cited by 35
- ringConGenstatement and proof · cited by 18
- iSup_Prop_eqproof · cited by 12
- RingCon.sSup_defproof · cited by 1
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