Theorems · Theorem · linear algebra
rank_quotient_add_rank_le
∀ {R : Type u} {M : Type v} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [Nontrivial R]
(M' : Submodule R M), Module.rank R (M ⧸ M') + Module.rank R ↥M' ≤ Module.rank R M- Cited by
- 1 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- Set.Elemproof · cited by 7,166
- Cardinalstatement and proof · cited by 2,598
- Nontrivialstatement and proof · cited by 2,416
- iSupproof · cited by 2,415
- HasQuotient.Quotientstatement and proof · cited by 2,301
- add_commproof · cited by 1,535
- Cardinal.mkproof · cited by 942
Cited by1
Results whose statement or proof uses this declaration.
- Module.finrank_quotient_add_finrank_leproof · cited by 0