Theorems · Theorem · linear algebra
Module.Basis.injective
∀ {ι : Type u_1} {R : Type u_3} {M : Type u_6} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
(b : Module.Basis ι R M) [Nontrivial R], Function.Injective ⇑b- Defined in
- Mathlib.LinearAlgebra.Basis.Defs
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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
- Nontrivialstatement and proof · cited by 2,416
- Module.Basisstatement and proof · cited by 1,477
- LinearEquiv.symmproof · cited by 1,461
- one_ne_zeroproof · cited by 885
- Module.Basis.reprproof · cited by 498
- LinearEquiv.injectiveproof · cited by 162
- Finsupp.single_left_injproof · cited by 4
Cited by12
Results whose statement or proof uses this declaration.
- Module.Basis.mk_eq_rank''proof · cited by 23
- Module.Basis.reindexRangeproof · cited by 16
- Module.Basis.mk_eq_rankproof · cited by 10
- rank_eq_card_basisproof · cited by 8
- ZLattice.rankproof · cited by 5
- Module.Basis.reindexRange_selfproof · cited by 4
- linearIndependent_le_basisproof · cited by 4
- Pi.dim_spanSubsetproof · cited by 2
- Submodule.rank_eq_spanRank_of_freeproof · cited by 2
- Module.Basis.maximalproof · cited by 1
- Module.Basis.reindexRange_repr'proof · cited by 1
- Module.Basis.le_spanproof · cited by 1