Theorems · Theorem · linear algebra
exists_set_linearIndependent
∀ (R : Type u_1) (M : Type u) [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
[HasRankNullity.{u, u_1} R], ∃ s, Cardinal.mk ↑s = Module.rank R M ∧ LinearIndependent (ι := ↑s) R Subtype.val- Cited by
- 2 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · 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
- Set.Elemstatement · cited by 7,166
- Cardinalstatement · cited by 2,598
- Cardinal.mkstatement · cited by 942
- LinearIndependentstatement · cited by 560
- Module.rankstatement · cited by 496
- HasRankNullitystatement and proof · cited by 26
- HasRankNullity.exists_set_linearIndependentproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- exists_linearIndepOn_of_lt_rankproof · cited by 1
- Submodule.span_range_eq_top_of_injective_of_rank_leproof · cited by 1