Theorems · Theorem · commutative algebra

LinearEquiv.mk.congr_simp

∀ {R : Type u_14} {S : Type u_15} [inst : Semiring R] [inst_1 : Semiring S] {σ : R →+* S} {σ' : S →+* R}
  [inst_2 : RingHomInvPair σ σ'] [inst_3 : RingHomInvPair σ' σ] {M : Type u_16} {M₂ : Type u_17}
  [inst_4 : AddCommMonoid M] [inst_5 : AddCommMonoid M₂] [inst_6 : Module R M] [inst_7 : Module S M₂]
  (toLinearMap toLinearMap_1 : M →ₛₗ[σ] M₂) (e_toLinearMap : toLinearMap = toLinearMap_1) (invFun invFun_1 : M₂ → M)
  (e_invFun : invFun = invFun_1) (left_inv : Function.LeftInverse invFun toLinearMap.toFun)
  (right_inv : Function.RightInverse invFun toLinearMap.toFun),
  { toLinearMap := toLinearMap, invFun := invFun, left_inv := left_inv, right_inv := right_inv } =
    { toLinearMap := toLinearMap_1, invFun := invFun_1, left_inv := ⋯, right_inv := ⋯ }

Defined in

Mathlib.Algebra.Module.Equiv.Basic

Cited by

12 results in Mathlib

Foundations

Depth 14 from the axioms · uses no axioms

Assumes

SemiringSemiringRingHomInvPairRingHomInvPairAddCommMonoidAddCommMonoidModuleModule