Theorems · Theorem · linear algebra

LinearMap.IsPerfectCompl.congr_simp

∀ {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 p_1 : M →ₗ[R] N →ₗ[R] R) (e_p : p = p_1) [inst_5 : p.IsPerfPair]
  (U U_1 : Submodule R M),
  U = U_1 → ∀ (V V_1 : Submodule R N), V = V_1 → p.IsPerfectCompl U V = p_1.IsPerfectCompl U_1 V_1

Defined in

Mathlib.LinearAlgebra.PerfectPairing.Restrict

Cited by

1 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleLinearMap.IsPerfPair