Theorems · Theorem · commutative algebra
Module.length_compositionSeries
∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
(s : CompositionSeries (Submodule R M)), RelSeries.head s = ⊥ → RelSeries.last s = ⊤ → ↑s.length = Module.length R M- Defined in
- Mathlib.RingTheory.Length
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites43
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Top.topstatement and proof · cited by 9,680
- Equivproof · cited by 8,337
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- Set.ofPredstatement and proof · cited by 6,101
- ENatstatement and proof · cited by 4,985
- Bot.botstatement and proof · cited by 4,720
- Equiv.symmproof · cited by 3,681
- LE.le.transproof · cited by 3,151
Cited by4
Results whose statement or proof uses this declaration.
- Module.length_ne_top_iffproof · cited by 8
- Module.length_eq_add_of_exactproof · cited by 6
- IsLocalRing.length_restrictScalarsproof · cited by 1
- IsLocalRing.length_baseChangeproof · cited by 1