Theorems · Theorem · linear algebra

LinearMap.IsPerfPair.restrict

∀ {R : Type u_1} {M : Type u_2} {N : Type u_3} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  [inst_3 : AddCommGroup N] [inst_4 : Module R N] (p : M →ₗ[R] N →ₗ[R] R) [inst_5 : p.IsPerfPair] {M' : Type u_4}
  {N' : Type u_5} [inst_6 : AddCommGroup M'] [inst_7 : Module R M'] [inst_8 : AddCommGroup N'] [inst_9 : Module R N']
  (i : M' →ₗ[R] M) (j : N' →ₗ[R] N),
  Function.Injective ⇑i → Function.Injective ⇑j → p.IsPerfectCompl i.range j.range → (p.compl₁₂ i j).IsPerfPair

The restriction of a perfect pairing to submodules is a perfect pairing.

Defined in

Mathlib.LinearAlgebra.PerfectPairing.Restrict

Cited by

1 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleLinearMap.IsPerfPairAddCommGroupModuleAddCommGroupModule