Theorems · Theorem · linear algebra
Module.Basis.coe_extend
∀ {K : Type u_3} {V : Type u_4} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] {s : Set V}
(hs : LinearIndepOn K id s), ⇑(Module.Basis.extend hs) = Subtype.val- Defined in
- Mathlib.LinearAlgebra.Basis.VectorSpace
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Set.Elemstatement · cited by 7,166
- Set.univstatement · cited by 3,945
- Module.Basisstatement · cited by 1,477
- DivisionRingstatement and proof · cited by 1,062
- Set.subset_univstatement · cited by 228
- LinearIndepOnstatement and proof · cited by 211
- LinearIndepOn.extendstatement · cited by 28
- Module.Basis.extendstatement · cited by 9
Cited by6
Results whose statement or proof uses this declaration.
- Submodule.eq_top_of_finrank_eqproof · cited by 15
- exists_nonarchimedean_pow_mul_seminorm_of_finiteDimensionalproof · cited by 5
- exists_subset_affineIndependent_affineSpan_eq_topproof · cited by 1
- Algebra.FormallyUnramified.range_eq_top_of_isPurelyInseparableproof · cited by 1
- Module.Basis.range_extendproof · cited by 1
- exists_basis_of_pairing_eq_zeroproof · cited by 0