Theorems · Theorem · sequences and series
multipliable_int_iff_multipliable_nat_and_neg
∀ {G : Type u_2} [inst : CommGroup G] [inst_1 : UniformSpace G] [IsUniformGroup G] [CompleteSpace G] {f : ℤ → G},
Multipliable f ↔ (Multipliable fun n => f ↑n) ∧ Multipliable fun n => f (-↑n)"iff" version of Multipliable.of_nat_of_neg.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CompleteSpacestatement and proof · cited by 2,532
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- UniformSpacestatement and proof · cited by 2,040
- CommGroupstatement and proof · cited by 990
- Multipliablestatement and proof · cited by 213
- IsUniformGroupstatement and proof · cited by 145
- Nat.cast_injectiveproof · cited by 39
- neg_injectiveproof · cited by 35
- Multipliable.comp_injectiveproof · cited by 7
- Multipliable.of_nat_of_negproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- tprod_int_eq_zero_mul_tprod_pnatproof · cited by 1