Theorems · Theorem · linear algebra
rank_fun
∀ {R : Type u} [inst : Semiring R] [StrongRankCondition R] {M η : Type u} [inst_2 : Fintype η]
[inst_3 : AddCommMonoid M] [inst_4 : Module R M] [Module.Free R M],
Module.rank R (η → M) = ↑(Fintype.card η) * Module.rank R M- Cited by
- 0 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
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
- Fintypestatement and proof · cited by 7,736
- Cardinalstatement and proof · cited by 2,598
- Fintype.cardstatement and proof · cited by 1,386
- Module.Freestatement and proof · cited by 597
- Module.rankstatement and proof · cited by 496
- StrongRankConditionstatement and proof · cited by 286
- Cardinal.mk_fintypeproof · cited by 81
- rank_piproof · cited by 6
- Cardinal.sum_const'proof · cited by 1
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