Theorems · Theorem · ring theory
IsGroupLikeElem.ne_zero
∀ {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] {a : A} [Nontrivial R], IsGroupLikeElem R a → a ≠ 0- Defined in
- Mathlib.RingTheory.Coalgebra.GroupLike
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext
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.
- Modulestatement and proof · cited by 20,661
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Nontrivialstatement and proof · cited by 2,416
- map_zeroproof · cited by 1,614
- Coalgebrastatement and proof · cited by 112
- CoalgebraStruct.counitproof · cited by 108
- IsGroupLikeElemstatement and proof · cited by 39
- IsGroupLikeElem.counit_eq_oneproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- linearIndepOn_isGroupLikeElemproof · cited by 3