Theorems · Theorem · group theory
Equiv.sum_comp
∀ {ι : Type u_1} {κ : Type u_2} {M : Type u_3} [inst : Fintype ι] [inst_1 : Fintype κ] [inst_2 : AddCommMonoid M]
(e : ι ≃ κ) (g : κ → M), ∑ i, g (e i) = ∑ i, g i- Cited by
- 31 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeFintypeAddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- AddCommMonoidstatement and proof · cited by 12,281
- Equivstatement and proof · cited by 8,337
- Fintypestatement and proof · cited by 7,736
- Finset.sumstatement · cited by 5,195
- Finset.univstatement · cited by 3,473
- Fintype.sum_equivproof · cited by 35
Cited by31
Results whose statement or proof uses this declaration.
- Fintype.sum_eq_add_sum_subtype_neproof · cited by 4
- jacobiSum_mul_nontrivialproof · cited by 3
- AnalyticOn.iteratedFDerivWithin_comp_permproof · cited by 3
- parallelepiped_comp_equivproof · cited by 3
- iteratedDerivWithin_vcomp_threeproof · cited by 2
- iteratedDerivWithin_vcomp_twoproof · cited by 2
- Equiv.vanishesTrivially_compproof · cited by 2
- TensorProduct.rTensor_injective_of_forall_vanishesTriviallyproof · cited by 2
- comp_equiv_symm_dotProductproof · cited by 2
- NumberField.Units.finrank_mul_regOfFamily_eq_detproof · cited by 2
- Module.length_pi_of_fintypeproof · cited by 2
- Matrix.trace_submatrix_succproof · cited by 1