Theorems · Theorem · group theory
finprod_cond_ne
∀ {α : Type u_1} {M : Type u_5} [inst : CommMonoid M] (f : α → M) (a : α) [inst_1 : DecidableEq α]
(hf : Function.HasFiniteMulSupport f), ∏ᶠ (i : α) (_ : i ≠ a), f i = ∏ i ∈ (Set.Finite.toFinset hf).erase a, f i- Defined in
- Mathlib.Algebra.BigOperators.Finprod
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidDecidableEq
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.
- Finset.prodstatement · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Finset.erasestatement · cited by 455
- Set.Finite.toFinsetstatement · cited by 351
- finprodstatement · cited by 257
- Function.mulSupportstatement · cited by 240
- Function.HasFiniteMulSupportstatement and proof · cited by 99
- Set.Finite.mem_toFinsetproof · cited by 74
- Finset.mem_eraseproof · cited by 61
- Function.mem_mulSupportproof · cited by 9
- finprod_cond_eq_prod_of_cond_iffproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.finprod_not_dvdproof · cited by 1