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Theorems · Theorem · general algebraic systems

Pi.single_comm

∀ {ι : Type u_1} [inst : DecidableEq ι] {M : Type u_9} [inst_1 : Zero M] (i : ι) (x : M) (j : ι),
  Pi.single i x j = Pi.single j x i

On non-dependent functions, Pi.single is symmetric in the two indices.

Defined in
Mathlib.Algebra.Notation.Pi.Basic
Cited by
2 results in Mathlib
Foundations
Depth 12 from the axioms · uses propext
Assumes
DecidableEqZero
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Matrix.mulVec_surjective_iff_exists_right_inverse · cited by 1Matrix.mulVec_surjective_…Matrix.cramer_one · cited by 1Matrix.cramer_onePi.single · cited by 518Pi.singlePi.single_apply · cited by 78Pi.single_applyPi.single_commCITED BYCITES

Cites2

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.