Theorems · Theorem · linear algebra
Module.rank_eq_ofNat_iff_finrank_eq_ofNat
∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (n : ℕ)
[inst_3 : n.AtLeastTwo], Module.rank R M = OfNat.ofNat n ↔ Module.finrank R M = OfNat.ofNat nThis is like rank_eq_one_iff_finrank_eq_one but works for 2, 3, 4, ...
- Defined in
- Mathlib.LinearAlgebra.Dimension.Finrank
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
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- 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
- Module.rankstatement · cited by 496
- Nat.AtLeastTwostatement and proof · cited by 405
- Cardinal.toNat_eq_ofNatproof · cited by 3
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