Theorems · Theorem · linear algebra
Subspace.dualLift_of_subtype
∀ {K : Type u_1} {V : Type u_2} [inst : Field K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] {W : Subspace K V}
{φ : Module.Dual K ↥W} (w : ↥W), (W.dualLift φ) ↑w = φ w- Defined in
- Mathlib.LinearAlgebra.Dual.Lemmas
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldAddCommGroupModule
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
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- Fieldstatement and proof · cited by 7,404
- Module.Dualstatement and proof · cited by 583
- Subspacestatement and proof · cited by 56
- Submodule.ker_subtypeproof · cited by 25
- Subspace.dualLiftstatement · cited by 9
- LinearMap.leftInverse_apply_of_injproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Subspace.dualRestrict_comp_dualLiftproof · cited by 1
- Subspace.dualPairing_nondegenerateproof · cited by 0
- Subspace.dualLift_of_memproof · cited by 0