Theorems · Theorem · group theory
DirectSum.Decomposition.isInternal
∀ {ι : Type u_1} {M : Type u_3} {σ : Type u_4} [inst : DecidableEq ι] [inst_1 : AddCommMonoid M] [inst_2 : SetLike σ M]
[inst_3 : AddSubmonoidClass σ M] (ℳ : ι → σ) [DirectSum.Decomposition ℳ], DirectSum.IsInternal ℳ- Defined in
- Mathlib.Algebra.DirectSum.Decomposition
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- SetLikestatement and proof · cited by 1,084
- AddSubmonoidClassstatement and proof · cited by 346
- DirectSum.IsInternalstatement · cited by 65
- DirectSum.Decompositionstatement and proof · cited by 57
- Function.LeftInverse.surjectiveproof · cited by 22
- Function.RightInverse.injectiveproof · cited by 20
- DirectSum.Decomposition.left_invproof · cited by 1
- DirectSum.Decomposition.right_invproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- DirectSum.Decomposition.inductionOnproof · cited by 2
- CliffordAlgebra.iSup_ι_range_eq_topproof · cited by 1
- CliffordAlgebra.evenOdd_isComplproof · cited by 0
- AddMonoidAlgebra.grade.isInternalproof · cited by 0
- DirectSum.IsInternal.baseChangeproof · cited by 0
- AddMonoidAlgebra.gradeBy.isInternalproof · cited by 0