Theorems · Theorem · general algebraic systems
Pi.mulSingle_eq_of_ne
∀ {ι : Type u_1} {M : ι → Type u_6} [inst : (i : ι) → One (M i)] [inst_1 : DecidableEq ι] {i i' : ι},
i' ≠ i → ∀ (x : M i), Pi.mulSingle i x i' = 1- Defined in
- Mathlib.Algebra.Notation.Pi.Basic
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- OneDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Function.update_of_neproof · cited by 198
- Pi.mulSinglestatement · cited by 111
Cited by14
Results whose statement or proof uses this declaration.
- MonoidHom.noncommPiCoprod_mulSingleproof · cited by 3
- Pi.mulSingle_eq_of_ne'proof · cited by 2
- Finset.noncommProd_mulSingleproof · cited by 2
- Pi.mulSingle_commuteproof · cited by 1
- Pi.mulSupport_mulSingle_subsetproof · cited by 1
- Subgroup.commutator_pi_pi_of_finiteproof · cited by 1
- Submonoid.pi_mem_of_mulSingle_mem_auxproof · cited by 1
- Pi.apply_mulSingle₂proof · cited by 1
- Fin.insertNth_one_rightproof · cited by 0
- Pi.update_eq_div_mul_mulSingleproof · cited by 0
- RestrictedProduct.mulSingle_eq_of_neproof · cited by 0
- Subgroup.closure_piproof · cited by 0