Theorems · Theorem · group theory
Con.sup_def
∀ {M : Type u_1} [inst : Mul M] (c d : Con M), c ⊔ d = conGen (⇑c ⊔ ⇑d)The supremum of two congruence relations equals the smallest congruence relation containing the supremum of the underlying binary operations.
- Defined in
- Mathlib.GroupTheory.Congruence.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Mul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Constatement and proof · cited by 152
- conGenstatement · cited by 23
- GaloisInsertion.l_sup_uproof · cited by 11
- Con.giproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- Con.sup_eq_conGenproof · cited by 0