Theorems · Theorem · linear algebra
Module.Basis.reindexRange_apply
∀ {ι : Type u_10} {R : Type u_11} {M : Type u_12} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
(b : Module.Basis ι R M) (x : ↑(Set.range ⇑b)), b.reindexRange x = ↑x- Defined in
- Mathlib.LinearAlgebra.Basis.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 84 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Set.Elemstatement and proof · cited by 7,166
- Set.rangestatement and proof · cited by 4,705
- Module.Basisstatement and proof · cited by 1,477
- Set.mem_range_selfproof · cited by 328
- Module.Basis.reindexRangestatement · cited by 16
- Module.Basis.reindexRange_selfproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Module.Basis.mk_eq_rank''proof · cited by 23
- Module.Basis.reindexFinsetRange_selfproof · cited by 1
- le_rank_iff_exists_linearIndependentproof · cited by 1