Theorems · Theorem · linear algebra
natCast_le_rank_iff
∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [Nontrivial R] {n : ℕ},
↑n ≤ Module.rank R M ↔ ∃ f, LinearIndependent R f- Defined in
- Mathlib.LinearAlgebra.Dimension.Finite
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
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- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Cardinalstatement · cited by 2,598
- Nontrivialstatement and proof · cited by 2,416
- Cardinal.liftproof · cited by 583
- LinearIndependentstatement and proof · cited by 560
- Module.rankstatement and proof · cited by 496
- Fintype.card_finproof · cited by 270
- Cardinal.mk_fintypeproof · cited by 81
- Cardinal.lift_natCastproof · cited by 39
- Cardinal.lift_uzeroproof · cited by 31
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