Theorems · Theorem · linear algebra
LinearMap.finrank_le_finrank_of_injective
∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [StrongRankCondition R]
{M' : Type u_2} [inst_4 : AddCommMonoid M'] [inst_5 : Module R M'] [Module.Finite R M'] {f : M →ₗ[R] M'},
Function.Injective ⇑f → Module.finrank R M ≤ Module.finrank R M'- Cited by
- 2 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement and proof · cited by 10,215
- Module.finrankstatement · cited by 1,770
- Module.Finitestatement and proof · cited by 1,032
- StrongRankConditionstatement and proof · cited by 286
- Module.rank_lt_aleph0proof · cited by 23
- Module.finrank_le_finrank_of_rank_le_rankproof · cited by 7
- LinearMap.lift_rank_le_of_injectiveproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- Subalgebra.LinearDisjoint.of_finrank_coprime_of_freeproof · cited by 1
- Submodule.finiteQuotient_iffproof · cited by 1