Theorems · Theorem · group theory
DirectSum.id_apply
∀ {M : Type v} {ι : Type u_1} [inst : AddCommMonoid M] [inst_1 : Unique ι] (x : DirectSum ι fun x => M),
(DirectSum.id M ι) x = x default- Defined in
- Mathlib.Algebra.DirectSum.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoidUnique
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- AddCommMonoidstatement and proof · cited by 12,281
- map_zeroproof · cited by 1,614
- AddEquivstatement · cited by 1,087
- map_addproof · cited by 964
- DFinsuppstatement · cited by 694
- DirectSumstatement and proof · cited by 446
- Uniquestatement and proof · cited by 400
- DirectSum.ofproof · cited by 122
- Unique.eq_defaultproof · cited by 38
- DirectSum.of_eq_sameproof · cited by 12
- AddEquiv.eq_symm_applyproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- DirectSum.lid_applyproof · cited by 0