Theorems · Theorem · commutative algebra
Submodule.spanFinrank_span_le_ncard_of_finite
∀ {R : Type u_1} {M : Type u} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {s : Set M},
s.Finite → (Submodule.span R s).spanFinrank ≤ s.ncard- Defined in
- Mathlib.Algebra.Module.SpanRank
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Set.Finitestatement and proof · cited by 1,814
- Submodule.spanstatement · cited by 1,504
- le_transproof · cited by 985
- Eq.geproof · cited by 375
- Set.ncardstatement · cited by 344
- Nat.cast_leproof · cited by 159
- Submodule.spanFinrankstatement · cited by 49
- Set.Finite.cast_ncard_eqproof · cited by 28
Cited by5
Results whose statement or proof uses this declaration.
- Submodule.spanFinrank_singletonproof · cited by 1
- TensorProduct.spanFinrank_top_eq_of_residueFieldproof · cited by 1