Theorems · Theorem · linear algebra
Module.one_lt_rank_of_one_lt_finrank
∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],
1 < Module.finrank R M → 1 < Module.rank R M- Defined in
- Mathlib.LinearAlgebra.Dimension.Finrank
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 94 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- Nat.cast_oneproof · cited by 2,501
- Module.finrankstatement and proof · cited by 1,770
- Module.rankstatement and proof · cited by 496
- Module.lt_rank_of_lt_finrankproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- exists_linearIndependent_pair_of_one_lt_finrankproof · cited by 0