Theorems · Theorem · linear algebra
Module.lt_rank_of_lt_finrank
∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {n : ℕ},
n < Module.finrank R M → ↑n < Module.rank R M- 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.
Cites13
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 and proof · cited by 1,770
- Cardinal.aleph0proof · cited by 521
- 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_apply_of_aleph0_leproof · cited by 9
Cited by3
Results whose statement or proof uses this declaration.
- Module.one_lt_rank_of_one_lt_finrankproof · cited by 1
- exists_linearIndependent_snoc_of_lt_finrankproof · cited by 0
- exists_linearIndependent_cons_of_lt_finrankproof · cited by 0