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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.Opposite.decl.json

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+[{"id":{"original":true,"range":[732,757]},"kind":"instance","modifiers":{"attrs":[],"computeKind":"regular","docString":["Like `Semiring.toModule`, but multiplies on the right. ",false],"isProtected":false,"isUnsafe":false,"recKind":"default","stx":[643,704],"visibility":"regular"},"name":["Semiring","toOppositeModule"],"params":[],"ref":{"original":true,"pp":"/-- Like `Semiring.toModule`, but multiplies on the right. -/\ninstance (priority := 910) toOppositeModule : Module Rᵐᵒᵖ R :=\n  {\n    MonoidWithZero.toOppositeMulActionWithZero\n      R with\n    smul_add := fun _ _ _ => add_mul _ _ _\n    add_smul := fun _ _ _ => mul_add _ _ _ }","range":[643,924]},"scopeInfo":{"currNamespace":["Semiring"],"includeVars":[],"levelNames":[],"omitVars":[],"openDecl":[],"scopedOpenDecl":[["Semiring"]],"varDecls":["variable {R M : Type*}","variable [Semiring R]","variable\n  [AddCommMonoid M]\n    -- see Note [lower instance priority]\n    "]},"signature":{"original":true,"pp":" : Module Rᵐᵒᵖ R","range":[758,779]},"type":{"original":true,"pp":"Module Rᵐᵒᵖ R","range":[760,779]},"value":{"original":true,"pp":" :=\n  {\n    MonoidWithZero.toOppositeMulActionWithZero\n      R with\n    smul_add := fun _ _ _ => add_mul _ _ _\n    add_smul := fun _ _ _ => mul_add _ _ _ }","range":[780,924]}},{"id":{"original":true,"range":[1117,1127]},"kind":"instance","modifiers":{"attrs":[],"computeKind":"regular","docString":["`MulOpposite.distribMulAction` extends to a `Module` ",false],"isProtected":false,"isUnsafe":false,"recKind":"default","stx":[1048,1107],"visibility":"regular"},"name":["MulOpposite","instModule"],"params":[],"ref":{"original":true,"pp":"/-- `MulOpposite.distribMulAction` extends to a `Module` -/\ninstance instModule : Module R Mᵐᵒᵖ\n    where\n  add_smul _ _ _ := unop_injective <| add_smul _ _ _\n  zero_smul _ := unop_injective <| zero_smul _ _","range":[1048,1257]},"scopeInfo":{"currNamespace":["MulOpposite"],"includeVars":[],"levelNames":[["v"],["u"]],"omitVars":[],"openDecl":[],"scopedOpenDecl":[["MulOpposite"]],"varDecls":["variable (R : Type u)","variable {M : Type v}","variable [Semiring R]","variable [AddCommMonoid M]","variable [Module R M]"]},"signature":{"original":true,"pp":" : Module R Mᵐᵒᵖ","range":[1128,1149]},"type":{"original":true,"pp":"Module R Mᵐᵒᵖ","range":[1130,1149]},"value":{"original":true,"pp":" where\n  add_smul _ _ _ := unop_injective <| add_smul _ _ _\n  zero_smul _ := unop_injective <| zero_smul _ _","range":[1150,1257]}}]

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.Opposite.mod.json

@@ -0,0 +1 @@
+{"docstring":["# Module operations on `Mᵐᵒᵖ`\n\nThis file contains definitions that build on top of the group action definitions in\n`Mathlib/Algebra/GroupWithZero/Action/Opposite.lean`.\n"],"imports":[["Init"],["Mathlib","Algebra","GroupWithZero","Action","Opposite"],["Mathlib","Algebra","Module","Defs"],["Mathlib","Algebra","Ring","Opposite"]]}

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.LinearAlgebra.Dual.Lemmas.decl.json

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