Theorems · Theorem · commutative algebra
Submodule.spanRank_span_le_card
∀ {R : Type u_1} {M : Type u} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (s : Set M),
(Submodule.span R s).spanRank ≤ Cardinal.mk ↑s- Defined in
- Mathlib.Algebra.Module.SpanRank
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 77 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.
Cites10
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.Elemstatement and proof · cited by 7,166
- Cardinalstatement and proof · cited by 2,598
- Submodule.spanstatement and proof · cited by 1,504
- Cardinal.mkstatement and proof · cited by 942
- Submodule.spanRankstatement · cited by 61
- ciInf_le'proof · cited by 6
Cited by10
Results whose statement or proof uses this declaration.
- Submodule.spanFinrank_span_le_encardproof · cited by 4
- Ideal.height_le_card_of_mem_minimalPrimes_span_finsetproof · cited by 3
- Submodule.lift_spanRank_le_iff_exists_span_set_card_leproof · cited by 3
- Submodule.lift_spanRank_map_eq_of_injectiveproof · cited by 2
- Submodule.spanRank_baseChange_leproof · cited by 2
- Submodule.spanRank_span_range_of_linearIndependentproof · cited by 1
- IsLocalRing.rank_cotangentSpace_eq_spanrank_maximalIdeal_of_fgproof · cited by 1
- Submodule.le_spanRank_restrictScalarsproof · cited by 1
- exists_spanRank_le_and_le_height_of_le_heightproof · cited by 1
- Submodule.spanRank_restrictScalars_eqproof · cited by 0