Theorems · Theorem · linear algebra
Module.apply_evalEquiv_symm_apply
∀ (R : Type u_3) (M : Type u_4) [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [inst_3 : Module.IsReflexive R M] (f : Module.Dual R M) (g : Module.Dual R (Module.Dual R M)), f ((Module.evalEquiv R M).symm g) = g f
- Defined in
- Mathlib.LinearAlgebra.Dual.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 40 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 and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearEquivstatement · cited by 3,317
- LinearEquiv.symmstatement and proof · cited by 1,461
- Module.Dualstatement and proof · cited by 583
- LinearEquiv.apply_symm_applyproof · cited by 108
- Module.IsReflexivestatement and proof · cited by 58
- Module.evalEquivstatement and proof · cited by 14
- Module.Dual.eval_applyproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- FiniteDimensional.mem_span_of_iInf_ker_le_kerproof · cited by 1
- LinearEquiv.trans_dualMap_symm_flipproof · cited by 1
- Module.symm_dualMap_evalEquivproof · cited by 0
- Submodule.span_eq_top_of_ne_zeroproof · cited by 0