Theorems · Theorem · linear algebra
Module.finrank_le_of_rank_le
∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {n : ℕ},
Module.rank R M ≤ ↑n → Module.finrank R M ≤ n- Defined in
- Mathlib.LinearAlgebra.Dimension.Finrank
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 93 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- 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
- Module.finrankstatement · cited by 1,770
- LE.le.trans_ltproof · cited by 795
- Module.rankstatement and proof · cited by 496
- Cardinal.toNatproof · cited by 153
- Cardinal.natCast_lt_aleph0proof · cited by 47
- Cardinal.toNat_natCastproof · cited by 19
- Cardinal.toNat_le_iff_le_of_lt_aleph0proof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- finrank_span_le_cardproof · cited by 8
- Projectivization.IsCollinear_iff_rankproof · cited by 1
- RCLike.finrank_le_twoproof · cited by 0