Theorems · Theorem · ring theory
CompleteOrthogonalIdempotents.single
∀ {I : Type u_4} [inst : Fintype I] [inst_1 : DecidableEq I] (R : I → Type u_5) [inst_2 : (i : I) → Semiring (R i)],
CompleteOrthogonalIdempotents fun x => Pi.single x 1- Defined in
- Mathlib.RingTheory.Idempotents
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableEqSemiring
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.
- Semiringstatement and proof · cited by 13,802
- Fintypestatement and proof · cited by 7,736
- mul_oneproof · cited by 3,885
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- Pi.singlestatement and proof · cited by 518
- Pi.single_eq_sameproof · cited by 144
- Pi.single_eq_of_neproof · cited by 116
- Pi.single_eq_of_ne'proof · cited by 33
- CompleteOrthogonalIdempotentsstatement · cited by 27
- Finset.univ_sum_singleproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.FormallySmooth.pi_iffproof · cited by 1