Theorems · Theorem · group theory
AddChar.exists_apply_ne_zero
∀ {α : Type u_1} [inst : AddCommGroup α] {a : α} [Finite α], (∃ ψ, ψ a ≠ 1) ↔ a ≠ 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 240 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroupFinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- AddCommGroupstatement and proof · cited by 12,871
- Complexstatement and proof · cited by 5,565
- Finset.sumproof · cited by 5,195
- mul_oneproof · cited by 3,885
- Finset.univproof · cited by 3,473
- Finitestatement and proof · cited by 3,029
- Finset.sum_congrproof · cited by 2,323
- one_ne_zeroproof · cited by 885
- Module.Basis.reprproof · cited by 498
- AddCharstatement and proof · cited by 286
- Module.Basis.sum_reprproof · cited by 29
Cited by1
Results whose statement or proof uses this declaration.
- AddChar.forall_apply_eq_zeroproof · cited by 1