Theorems · Theorem · linear algebra
LinearMap.apply_symm_toPerfPair_self
∀ {R : Type u_1} {M : Type u_3} {N : Type u_5} [inst : AddCommGroup M] [inst_1 : AddCommGroup N] [inst_2 : CommRing R]
[inst_3 : Module R M] [inst_4 : Module R N] (p : M →ₗ[R] N →ₗ[R] R) [inst_5 : p.IsPerfPair] (f : Module.Dual R N),
p (p.toPerfPair.symm f) = f- Cited by
- 2 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- RingHom.idstatement and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- LinearEquivstatement · cited by 3,317
- LinearEquiv.symmstatement · cited by 1,461
- Module.Dualstatement and proof · cited by 583
- LinearEquiv.apply_symm_applyproof · cited by 108
- LinearMap.toPerfPairstatement and proof · cited by 46
- LinearMap.IsPerfPairstatement and proof · cited by 34
Cited by2
Results whose statement or proof uses this declaration.
- RootPairing.toPerfPair_conj_reflectionproof · cited by 2
- LinearMap.apply_toPerfPair_flipproof · cited by 1