Theorems · Theorem · commutative algebra

LinearEquiv.congrLeft_symm_apply

∀ (M : Type u_5) {M₂ : Type u_7} {M₃ : Type u_8} [inst : AddCommMonoid M] [inst_1 : AddCommMonoid M₂]
  [inst_2 : AddCommMonoid M₃] {R : Type u_9} (S : Type u_10) [inst_3 : Semiring R] [inst_4 : Semiring S]
  [inst_5 : Module R M₂] [inst_6 : Module R M₃] [inst_7 : Module R M] [inst_8 : Module S M]
  [inst_9 : SMulCommClass R S M] (e : M₂ ≃ₗ[R] M₃) (a : M₃ →ₗ[R] M),
  (LinearEquiv.congrLeft M S e).symm a = (e.arrowCongrAddEquiv (LinearEquiv.refl R M)).invFun a

Defined in

Mathlib.Algebra.Module.Equiv.Basic

Cited by

0 results in Mathlib

Foundations

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

Assumes

AddCommMonoidAddCommMonoidAddCommMonoidSemiringSemiringModuleModuleModuleModuleSMulCommClass