Theorems · Theorem · linear algebra
HasRankNullity.exists_set_linearIndependent
∀ {R : Type v} {inst : Ring R} [self : HasRankNullity.{u, v} R] (M : Type u) [inst_1 : AddCommGroup M]
[inst_2 : Module R M], ∃ s, Cardinal.mk ↑s = Module.rank R M ∧ LinearIndepOn R id s- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
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 · cited by 53,352
- Modulestatement · cited by 20,661
- AddCommGroupstatement · 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
- Module.rankstatement · cited by 496
- LinearIndepOnstatement · cited by 211
- HasRankNullitystatement and proof · cited by 26
Cited by1
Results whose statement or proof uses this declaration.
- exists_set_linearIndependentproof · cited by 2