Theorems · Theorem · linear algebra
Module.finrank_eq_of_rank_eq
∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {n : ℕ},
Module.rank R M = ↑n → Module.finrank R M = n- Defined in
- Mathlib.LinearAlgebra.Dimension.Finrank
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 91 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.
Cites9
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 · cited by 1,770
- Module.rankstatement and proof · cited by 496
- Cardinal.toNatproof · cited by 153
- Cardinal.toNat_natCastproof · cited by 19
Cited by13
Results whose statement or proof uses this declaration.
- Module.finrank_eq_card_basisproof · cited by 40
- Module.finrank_selfproof · cited by 24
- finrank_botproof · cited by 18
- Module.finrank_fintype_fun_eq_cardproof · cited by 14
- finrank_span_eq_cardproof · cited by 7
- finrank_span_set_eq_cardproof · cited by 4
- CommSemiring.finrank_selfproof · cited by 3
- finrank_eq_oneproof · cited by 1
- MvPolynomial.finrank_Rproof · cited by 1
- RatFunc.finrank_ratFunc_ratFuncproof · cited by 1
- Submodule.IsLattice.finrank_of_piproof · cited by 0
- Subalgebra.finrank_botproof · cited by 0