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Theorems · Theorem · group theory

DirectSum.id_symm_apply

∀ {M : Type v} {ι : Type u_1} [inst : AddCommMonoid M] [inst_1 : Unique ι] (x : M),
  (DirectSum.id M ι).symm x = (DirectSum.of (fun i => M) default) x
Defined in
Mathlib.Algebra.DirectSum.Basic
Cited by
2 results in Mathlib
Foundations
Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommMonoidUnique
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

DirectSum.lid_symm_apply · cited by 2DirectSum.lid_symm_applyDirectSum.id_apply · cited by 1DirectSum.id_applyDFunLike.coe · cited by 62936DFunLike.coeAddCommMonoid · cited by 12281AddCommMonoidAddMonoidHom · cited by 3230AddMonoidHomAddEquiv · cited by 1087AddEquivAddEquiv.symm · cited by 530AddEquiv.symmDirectSum · cited by 446DirectSumUnique · cited by 400UniqueDirectSum.of · cited by 122DirectSum.ofDirectSum.id · cited by 2DirectSum.idDirectSum.id_symm_applyCITED BYCITES

Cites9

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Cited by2

Results whose statement or proof uses this declaration.