Theorems · Definition · ring theory

GroupLike.casesOn

{R : Type u_2} →
  {A : Type u_3} →
    [inst : CommSemiring R] →
      [inst_1 : AddCommMonoid A] →
        [inst_2 : Module R A] →
          [inst_3 : Coalgebra R A] →
            {motive : GroupLike R A → Sort u} →
              (t : GroupLike R A) →
                ((val : A) →
                    (isGroupLikeElem_val : IsGroupLikeElem R val) →
                      motive { val := val, isGroupLikeElem_val := isGroupLikeElem_val }) →
                  motive t

Defined in: Mathlib.RingTheory.Coalgebra.GroupLike
Cited by: 1 results in Mathlib
Foundations: Depth 6 from the axioms · uses no axioms
Assumes: CommSemiring AddCommMonoid Module Coalgebra

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Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Modulestatement and proof · cited by 20,661
AddCommMonoidstatement and proof · cited by 12,281
CommSemiringstatement and proof · cited by 10,911
Coalgebrastatement and proof · cited by 112
IsGroupLikeElemstatement and proof · cited by 39
GroupLikestatement and proof · cited by 19

Cited by3

Results whose statement or proof uses this declaration.

GroupLike.val_injectiveproof · cited by 1
GroupLike.noConfusionproof · cited by 0
GroupLike.noConfusionTypeproof · cited by 0