Theorems · Theorem · group theory
AddAction.fixedBy_eq_univ_iff_eq_zero
∀ {α : Type u_1} {M : Type u_3} [inst : AddMonoid M] [inst_1 : AddAction M α] [FaithfulVAdd M α] {m : M},
AddAction.fixedBy α m = Set.univ ↔ m = 0If the additive action of M on α is faithful,
then fixedBy α m = Set.univ implies that m = 1.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.univstatement and proof · cited by 3,945
- AddMonoidstatement and proof · cited by 2,864
- HVAdd.hVAddproof · cited by 1,820
- AddActionstatement and proof · cited by 820
- zero_vaddproof · cited by 95
- Set.eq_univ_iff_forallproof · cited by 93
- AddAction.fixedBystatement and proof · cited by 26
- FaithfulVAddstatement and proof · cited by 17
- AddAction.mem_fixedByproof · cited by 12
- vadd_left_injective'proof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- AddAction.not_addCommute_of_disjoint_movedBy_preimageproof · cited by 0