Theorems · Theorem · group theory
CommGroup.forall_apply_eq_apply_iff
∀ (G : Type u_1) {M : Type u_2} [inst : CommGroup G] [Finite G] [inst_2 : CommMonoid M]
[hM : HasEnoughRootsOfUnity M (Monoid.exponent G)] {g g' : G}, (∀ (φ : G →* Mˣ), φ g = φ g') ↔ g = g'- Cited by
- 1 results in Mathlib
- Foundations
- Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- MonoidHomstatement and proof · cited by 3,629
- Finitestatement and proof · cited by 3,029
- Unitsstatement and proof · cited by 2,804
- CommMonoidstatement and proof · cited by 2,264
- map_mulproof · cited by 1,137
- CommGroupstatement and proof · cited by 990
- Monoid.exponentstatement and proof · cited by 128
- mul_inv_cancelproof · cited by 128
- map_invproof · cited by 95
- HasEnoughRootsOfUnitystatement and proof · cited by 56
- CommGroup.exists_apply_ne_one_of_hasEnoughRootsOfUnityproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- CommGroup.forall_monoidHom_apply_eq_one_iffproof · cited by 0