Theorems · Theorem · linear algebra
rank_finsupp
∀ (R : Type u) (M : Type v) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [StrongRankCondition R]
[Module.Free R M] (ι : Type w),
Module.rank R (ι →₀ M) = Cardinal.lift.{v, w} (Cardinal.mk ι) * Cardinal.lift.{w, v} (Module.rank R M)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Finsuppstatement and proof · cited by 5,255
- Cardinalstatement and proof · cited by 2,598
- Module.Basisproof · cited by 1,477
- Cardinal.mkstatement and proof · cited by 942
- Module.Freestatement and proof · cited by 597
- Cardinal.liftstatement and proof · cited by 583
- Module.rankstatement and proof · cited by 496
- StrongRankConditionstatement and proof · cited by 286
- Module.Free.exists_basisproof · cited by 26
Cited by4
Results whose statement or proof uses this declaration.
- rank_finsupp_selfproof · cited by 3
- rank_finsupp_self'proof · cited by 1
- Module.finrank_finsuppproof · cited by 0
- rank_finsupp'proof · cited by 0