Theorems · Theorem · ring theory
CompleteOrthogonalIdempotents.prod_one_sub
∀ {R : Type u_1} [inst : CommRing R] {I : Type u_3} [inst_1 : Fintype I] {e : I → R},
CompleteOrthogonalIdempotents e → ∏ i, (1 - e i) = 0- Defined in
- Mathlib.RingTheory.Idempotents
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Fintypestatement and proof · cited by 7,736
- Finset.univstatement and proof · cited by 3,473
- Finset.prodstatement · cited by 2,356
- sub_selfproof · cited by 996
- CompleteOrthogonalIdempotentsstatement and proof · cited by 27
- CompleteOrthogonalIdempotents.toOrthogonalIdempotentsproof · cited by 7
- CompleteOrthogonalIdempotents.completeproof · cited by 4
- OrthogonalIdempotents.prod_one_subproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- CompleteOrthogonalIdempotents.bijective_piproof · cited by 2