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Mathlib.Algebra.Module.Opposites

Module operations on Mᵐᵒᵖ #

This file contains definitions that build on top of the group action definitions in GroupTheory.GroupAction.Opposite.

The function op is a linear equivalence.

Equations
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Instances For
    @[simp]
    theorem MulOpposite.coe_opLinearEquiv (R : Type u) {M : Type v} [Semiring R] [AddCommMonoid M] [Module R M] :
    (MulOpposite.opLinearEquiv R) = MulOpposite.op
    @[simp]
    @[simp]
    theorem MulOpposite.coe_opLinearEquiv_toLinearMap (R : Type u) {M : Type v} [Semiring R] [AddCommMonoid M] [Module R M] :
    (MulOpposite.opLinearEquiv R) = MulOpposite.op
    @[simp]
    theorem MulOpposite.coe_opLinearEquiv_addEquiv (R : Type u) {M : Type v} [Semiring R] [AddCommMonoid M] [Module R M] :
    (MulOpposite.opLinearEquiv R) = MulOpposite.opAddEquiv