Submodule

📁 Source: Mathlib/LinearAlgebra/TensorProduct/Submodule.lean

Statistics

Metric	Count
Definitions lTensorOne, lTensorOne', mulMap, mulMap', rTensorOne, rTensorOne'	6
Theorems coe_mulMap_comp_eq, comm_trans_lTensorOne, comm_trans_rTensorOne, lTensorOne'_one_tmul, lTensorOne'_tmul, lTensorOne_one_tmul, lTensorOne_symm_apply, lTensorOne_tmul, mulLeftMap_eq_mulMap_comp, mulMap'_surjective, mulMap_comm, mulMap_comm_of_commute, mulMap_comp_lTensor, mulMap_comp_map_inclusion, mulMap_comp_rTensor, mulMap_eq_mul'_comp_mapIncl, mulMap_map_comp_eq, mulMap_one_left_eq, mulMap_one_right_eq, mulMap_op, mulMap_range, mulMap_tmul, mulRightMap_eq_mulMap_comp, rTensorOne'_tmul, rTensorOne'_tmul_one, rTensorOne_symm_apply, rTensorOne_tmul, rTensorOne_tmul_one, val_mulMap'_tmul	29
Total	35

Submodule

Definitions

Name	Category	Theorems
lTensorOne 📖	CompOp	6 math math: comm_trans_lTensorOne, comm_trans_rTensorOne, mulMap_one_left_eq, lTensorOne_symm_apply, lTensorOne_tmul, lTensorOne_one_tmul
lTensorOne' 📖	CompOp	2 math math: lTensorOne'_tmul, lTensorOne'_one_tmul
mulMap 📖	CompOp	19 math math: mulMap_tmul, mulMap_one_right_eq, Subalgebra.mulMap_toLinearMap, mulMap_comm, linearDisjoint_iff, LinearDisjoint.injective, mulRightMap_eq_mulMap_comp, coe_mulMap_comp_eq, mulMap_one_left_eq, mulMap_comm_of_commute, mulMap_eq_mul'_comp_mapIncl, mulLeftMap_eq_mulMap_comp, mulMap_map_comp_eq, Algebra.TensorProduct.linearEquivIncludeRange_symm_toLinearMap, mulMap_comp_lTensor, mulMap_comp_map_inclusion, mulMap_op, mulMap_range, mulMap_comp_rTensor
mulMap' 📖	CompOp	2 math math: val_mulMap'_tmul, mulMap'_surjective
rTensorOne 📖	CompOp	6 math math: rTensorOne_symm_apply, comm_trans_lTensorOne, mulMap_one_right_eq, comm_trans_rTensorOne, rTensorOne_tmul, rTensorOne_tmul_one
rTensorOne' 📖	CompOp	2 math math: rTensorOne'_tmul_one, rTensorOne'_tmul

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
coe_mulMap_comp_eq 📖	mathematical	—	TensorProduct Submodule CommSemiring.toSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring Algebra.toModule SetLike.instMembership setLike addCommMonoid module map RingHom.id RingHomSurjective.ids SemilinearMapClass.semilinearMap AlgHom AlgHom.funLike NonUnitalAlgHomClass.instLinearMapClass AlgHom.instNonUnitalAlgHomClassOfAlgHomClass AlgHom.algHomClass DFunLike.coe LinearMap TensorProduct.addCommMonoid TensorProduct.instModule LinearMap.instFunLike mulMap TensorProduct.map LinearMap.submoduleMap	—	RingHomSurjective.ids NonUnitalAlgHomClass.instLinearMapClass AlgHom.instNonUnitalAlgHomClassOfAlgHomClass AlgHom.algHomClass RingHomCompTriple.ids mulMap_map_comp_eq
comm_trans_lTensorOne 📖	mathematical	—	LinearEquiv.trans TensorProduct Submodule CommSemiring.toSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring Algebra.toModule SetLike.instMembership setLike Subalgebra Subalgebra.instSetLike Bot.bot OrderBot.toBot Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder Lattice.toSemilatticeSup CompleteLattice.toLattice Algebra.instCompleteLatticeSubalgebra BoundedOrder.toOrderBot CompleteLattice.toBoundedOrder addCommMonoid Subalgebra.toSemiring module Subalgebra.instModuleSubtypeMem TensorProduct.addCommMonoid TensorProduct.instModule RingHom.id RingHomCompTriple.ids RingHomInvPair.ids TensorProduct.comm lTensorOne rTensorOne	—	LinearEquiv.toLinearMap_injective RingHomInvPair.ids RingHomCompTriple.ids TensorProduct.ext' Algebra.mem_bot Subtype.val_injective IsScalarTower.left lTensorOne_tmul rTensorOne_tmul
comm_trans_rTensorOne 📖	mathematical	—	LinearEquiv.trans TensorProduct Subalgebra SetLike.instMembership Subalgebra.instSetLike Bot.bot OrderBot.toBot Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder Lattice.toSemilatticeSup CompleteLattice.toLattice Algebra.instCompleteLatticeSubalgebra BoundedOrder.toOrderBot CompleteLattice.toBoundedOrder Submodule CommSemiring.toSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring Algebra.toModule setLike Subalgebra.toSemiring addCommMonoid Subalgebra.instModuleSubtypeMem module TensorProduct.addCommMonoid TensorProduct.instModule RingHom.id RingHomCompTriple.ids RingHomInvPair.ids TensorProduct.comm rTensorOne lTensorOne	—	LinearEquiv.toLinearMap_injective RingHomInvPair.ids RingHomCompTriple.ids TensorProduct.ext' Algebra.mem_bot Subtype.val_injective IsScalarTower.left rTensorOne_tmul lTensorOne_tmul
lTensorOne'_one_tmul 📖	mathematical	—	DFunLike.coe LinearMap CommSemiring.toSemiring RingHom.id Semiring.toNonAssocSemiring TensorProduct Subalgebra SetLike.instMembership Subalgebra.instSetLike Bot.bot OrderBot.toBot Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder Lattice.toSemilatticeSup CompleteLattice.toLattice Algebra.instCompleteLatticeSubalgebra BoundedOrder.toOrderBot CompleteLattice.toBoundedOrder Submodule NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Algebra.toModule setLike Subalgebra.toSemiring addCommMonoid Subalgebra.instModuleSubtypeMem module TensorProduct.addCommMonoid TensorProduct.instModule LinearMap.instFunLike lTensorOne' TensorProduct.tmul OneMemClass.one AddMonoidWithOne.toOne AddCommMonoidWithOne.toAddMonoidWithOne NonAssocSemiring.toAddCommMonoidWithOne AddSubmonoidWithOneClass.toOneMemClass SubsemiringClass.addSubmonoidWithOneClass Subalgebra.instSubsemiringClass	—	IsScalarTower.left AddSubmonoidWithOneClass.toOneMemClass SubsemiringClass.addSubmonoidWithOneClass Subalgebra.instSubsemiringClass map_one MonoidHomClass.toOneHomClass MonoidWithZeroHomClass.toMonoidHomClass RingHomClass.toMonoidWithZeroHomClass RingHom.instRingHomClass one_smul lTensorOne'_tmul
lTensorOne'_tmul 📖	mathematical	—	DFunLike.coe LinearMap CommSemiring.toSemiring RingHom.id Semiring.toNonAssocSemiring TensorProduct Subalgebra SetLike.instMembership Subalgebra.instSetLike Bot.bot OrderBot.toBot Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder Lattice.toSemilatticeSup CompleteLattice.toLattice Algebra.instCompleteLatticeSubalgebra BoundedOrder.toOrderBot CompleteLattice.toBoundedOrder Submodule NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Algebra.toModule setLike Subalgebra.toSemiring addCommMonoid Subalgebra.instModuleSubtypeMem module TensorProduct.addCommMonoid TensorProduct.instModule LinearMap.instFunLike lTensorOne' TensorProduct.tmul RingHom RingHom.instFunLike algebraMap Subalgebra.algebra smul Algebra.toSMul Algebra.id IsScalarTower.left MonoidWithZero.toMonoid Semiring.toMonoidWithZero DistribMulAction.toMulAction AddCommMonoid.toAddMonoid Module.toDistribMulAction	—	Subtype.val_injective IsScalarTower.left Algebra.smul_def mulMap_tmul
lTensorOne_one_tmul 📖	mathematical	—	DFunLike.coe LinearEquiv CommSemiring.toSemiring RingHom.id Semiring.toNonAssocSemiring RingHomInvPair.ids TensorProduct Subalgebra SetLike.instMembership Subalgebra.instSetLike Bot.bot OrderBot.toBot Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder Lattice.toSemilatticeSup CompleteLattice.toLattice Algebra.instCompleteLatticeSubalgebra BoundedOrder.toOrderBot CompleteLattice.toBoundedOrder Submodule NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Algebra.toModule setLike Subalgebra.toSemiring addCommMonoid Subalgebra.instModuleSubtypeMem module TensorProduct.addCommMonoid TensorProduct.instModule EquivLike.toFunLike DFinsupp.instEquivLikeLinearEquiv lTensorOne TensorProduct.tmul OneMemClass.one AddMonoidWithOne.toOne AddCommMonoidWithOne.toAddMonoidWithOne NonAssocSemiring.toAddCommMonoidWithOne AddSubmonoidWithOneClass.toOneMemClass SubsemiringClass.addSubmonoidWithOneClass Subalgebra.instSubsemiringClass	—	lTensorOne'_one_tmul
lTensorOne_symm_apply 📖	mathematical	—	DFunLike.coe LinearEquiv CommSemiring.toSemiring RingHom.id Semiring.toNonAssocSemiring RingHomInvPair.ids Submodule NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Algebra.toModule SetLike.instMembership setLike TensorProduct Subalgebra Subalgebra.instSetLike Bot.bot OrderBot.toBot Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder Lattice.toSemilatticeSup CompleteLattice.toLattice Algebra.instCompleteLatticeSubalgebra BoundedOrder.toOrderBot CompleteLattice.toBoundedOrder Subalgebra.toSemiring addCommMonoid Subalgebra.instModuleSubtypeMem module TensorProduct.addCommMonoid TensorProduct.instModule EquivLike.toFunLike DFinsupp.instEquivLikeLinearEquiv LinearEquiv.symm lTensorOne TensorProduct.tmul OneMemClass.one AddMonoidWithOne.toOne AddCommMonoidWithOne.toAddMonoidWithOne NonAssocSemiring.toAddCommMonoidWithOne AddSubmonoidWithOneClass.toOneMemClass SubsemiringClass.addSubmonoidWithOneClass Subalgebra.instSubsemiringClass	—	RingHomInvPair.ids
lTensorOne_tmul 📖	mathematical	—	DFunLike.coe LinearEquiv CommSemiring.toSemiring RingHom.id Semiring.toNonAssocSemiring RingHomInvPair.ids TensorProduct Subalgebra SetLike.instMembership Subalgebra.instSetLike Bot.bot OrderBot.toBot Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder Lattice.toSemilatticeSup CompleteLattice.toLattice Algebra.instCompleteLatticeSubalgebra BoundedOrder.toOrderBot CompleteLattice.toBoundedOrder Submodule NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Algebra.toModule setLike Subalgebra.toSemiring addCommMonoid Subalgebra.instModuleSubtypeMem module TensorProduct.addCommMonoid TensorProduct.instModule EquivLike.toFunLike DFinsupp.instEquivLikeLinearEquiv lTensorOne TensorProduct.tmul RingHom RingHom.instFunLike algebraMap Subalgebra.algebra smul Algebra.toSMul Algebra.id IsScalarTower.left MonoidWithZero.toMonoid Semiring.toMonoidWithZero DistribMulAction.toMulAction AddCommMonoid.toAddMonoid Module.toDistribMulAction	—	lTensorOne'_tmul
mulLeftMap_eq_mulMap_comp 📖	mathematical	—	mulLeftMap CommSemiring.toSemiring Algebra.toModule smulCommClass_self CommSemiring.toCommMonoid DistribMulAction.toMulAction CommMonoid.toMonoid AddCommMonoid.toAddMonoid NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring Module.toDistribMulAction Algebra.to_smulCommClass LinearMap.comp Finsupp Submodule SetLike.instMembership setLike AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass addCommMonoid TensorProduct module Finsupp.instAddCommMonoid TensorProduct.addCommMonoid Finsupp.module TensorProduct.instModule RingHom.id RingHomCompTriple.ids mulMap MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass Semiring.toModule LinearMap.rTensor Finsupp.linearCombination LinearEquiv.toLinearMap RingHomInvPair.ids LinearEquiv.symm TensorProduct.finsuppScalarLeft	—	Finsupp.lhom_ext' smulCommClass_self Algebra.to_smulCommClass RingHomCompTriple.ids RingHomInvPair.ids LinearMap.ext mulLeftMap_apply_single TensorProduct.finsuppScalarLeft_symm_apply_single Finsupp.linearCombination_single one_smul
mulMap'_surjective 📖	mathematical	—	TensorProduct Submodule CommSemiring.toSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring Algebra.toModule SetLike.instMembership setLike addCommMonoid module mul IsScalarTower.right DFunLike.coe LinearMap RingHom.id TensorProduct.addCommMonoid TensorProduct.instModule LinearMap.instFunLike mulMap'	—	IsScalarTower.right mulMap_range
mulMap_comm 📖	mathematical	—	mulMap CommSemiring.toSemiring LinearMap.comp TensorProduct Submodule NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring Algebra.toModule SetLike.instMembership setLike addCommMonoid module TensorProduct.addCommMonoid TensorProduct.instModule RingHom.id RingHomCompTriple.ids LinearEquiv.toLinearMap RingHomInvPair.ids TensorProduct.comm	—	mulMap_comm_of_commute mul_comm
mulMap_comm_of_commute 📖	mathematical	Commute Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring Submodule CommSemiring.toSemiring NonUnitalNonAssocSemiring.toAddCommMonoid Algebra.toModule SetLike.instMembership setLike	mulMap LinearMap.comp TensorProduct addCommMonoid module TensorProduct.addCommMonoid TensorProduct.instModule RingHom.id RingHomCompTriple.ids LinearEquiv.toLinearMap RingHomInvPair.ids TensorProduct.comm	—	TensorProduct.ext' RingHomCompTriple.ids RingHomInvPair.ids Commute.symm
mulMap_comp_lTensor 📖	mathematical	Submodule CommSemiring.toSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring Algebra.toModule Preorder.toLE PartialOrder.toPreorder instPartialOrder	LinearMap.comp TensorProduct SetLike.instMembership setLike addCommMonoid module TensorProduct.addCommMonoid TensorProduct.instModule RingHom.id RingHomCompTriple.ids mulMap LinearMap.lTensor inclusion	—	TensorProduct.ext' RingHomCompTriple.ids
mulMap_comp_map_inclusion 📖	mathematical	Submodule CommSemiring.toSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring Algebra.toModule Preorder.toLE PartialOrder.toPreorder instPartialOrder	LinearMap.comp TensorProduct SetLike.instMembership setLike addCommMonoid module TensorProduct.addCommMonoid TensorProduct.instModule RingHom.id RingHomCompTriple.ids mulMap TensorProduct.map inclusion	—	TensorProduct.ext' RingHomCompTriple.ids
mulMap_comp_rTensor 📖	mathematical	Submodule CommSemiring.toSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring Algebra.toModule Preorder.toLE PartialOrder.toPreorder instPartialOrder	LinearMap.comp TensorProduct SetLike.instMembership setLike addCommMonoid module TensorProduct.addCommMonoid TensorProduct.instModule RingHom.id RingHomCompTriple.ids mulMap LinearMap.rTensor inclusion	—	TensorProduct.ext' RingHomCompTriple.ids
mulMap_eq_mul'_comp_mapIncl 📖	mathematical	—	mulMap LinearMap.comp TensorProduct Submodule CommSemiring.toSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring Algebra.toModule SetLike.instMembership setLike addCommMonoid module TensorProduct.addCommMonoid TensorProduct.instModule RingHom.id RingHomCompTriple.ids LinearMap.mul' Algebra.to_smulCommClass IsScalarTower.right TensorProduct.mapIncl	—	TensorProduct.ext' RingHomCompTriple.ids Algebra.to_smulCommClass IsScalarTower.right
mulMap_map_comp_eq 📖	mathematical	—	LinearMap.comp TensorProduct Submodule CommSemiring.toSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring Algebra.toModule SetLike.instMembership setLike addCommMonoid module map RingHom.id RingHomSurjective.ids SemilinearMapClass.semilinearMap AlgHom AlgHom.funLike NonUnitalAlgHomClass.instLinearMapClass AlgHom.instNonUnitalAlgHomClassOfAlgHomClass AlgHom.algHomClass TensorProduct.addCommMonoid TensorProduct.instModule RingHomCompTriple.ids mulMap TensorProduct.map LinearMap.submoduleMap	—	TensorProduct.AlgebraTensorModule.curry_injective isScalarTower' IsScalarTower.left RingHomSurjective.ids NonUnitalAlgHomClass.instLinearMapClass AlgHom.instNonUnitalAlgHomClassOfAlgHomClass AlgHom.algHomClass RingHomCompTriple.ids LinearMap.ext IsScalarTower.to_smulCommClass map_mul NonUnitalAlgSemiHomClass.toMulHomClass
mulMap_one_left_eq 📖	mathematical	—	mulMap DFunLike.coe OrderEmbedding Subalgebra Submodule CommSemiring.toSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring Algebra.toModule Preorder.toLE PartialOrder.toPreorder Subalgebra.instPartialOrder instPartialOrder instFunLikeOrderEmbedding Subalgebra.toSubmodule Bot.bot OrderBot.toBot SemilatticeSup.toPartialOrder Lattice.toSemilatticeSup CompleteLattice.toLattice Algebra.instCompleteLatticeSubalgebra BoundedOrder.toOrderBot CompleteLattice.toBoundedOrder LinearMap.comp TensorProduct SetLike.instMembership Subalgebra.instSetLike setLike Subalgebra.toSemiring addCommMonoid Subalgebra.instModuleSubtypeMem module TensorProduct.addCommMonoid TensorProduct.instModule RingHom.id RingHomCompTriple.ids subtype LinearEquiv.toLinearMap RingHomInvPair.ids lTensorOne	—	TensorProduct.ext' RingHomCompTriple.ids RingHomInvPair.ids
mulMap_one_right_eq 📖	mathematical	—	mulMap DFunLike.coe OrderEmbedding Subalgebra Submodule CommSemiring.toSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring Algebra.toModule Preorder.toLE PartialOrder.toPreorder Subalgebra.instPartialOrder instPartialOrder instFunLikeOrderEmbedding Subalgebra.toSubmodule Bot.bot OrderBot.toBot SemilatticeSup.toPartialOrder Lattice.toSemilatticeSup CompleteLattice.toLattice Algebra.instCompleteLatticeSubalgebra BoundedOrder.toOrderBot CompleteLattice.toBoundedOrder LinearMap.comp TensorProduct SetLike.instMembership setLike Subalgebra.instSetLike addCommMonoid Subalgebra.toSemiring module Subalgebra.instModuleSubtypeMem TensorProduct.addCommMonoid TensorProduct.instModule RingHom.id RingHomCompTriple.ids subtype LinearEquiv.toLinearMap RingHomInvPair.ids rTensorOne	—	TensorProduct.ext' RingHomCompTriple.ids RingHomInvPair.ids
mulMap_op 📖	mathematical	—	mulMap MulOpposite MulOpposite.instSemiring MulOpposite.instAlgebra DFunLike.coe RingEquiv Submodule CommSemiring.toSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring Algebra.toModule MulOpposite.instAddCommMonoid MulOpposite.instModule MulOpposite.instMul mul IsScalarTower.right MulOpposite.instAdd pointwiseAdd EquivLike.toFunLike RingEquiv.instEquivLike RingEquiv.symm equivOpposite MulOpposite.op LinearMap.comp TensorProduct SetLike.instMembership setLike comap RingHom.id LinearEquiv.toLinearMap RingHomInvPair.ids LinearEquiv.symm MulOpposite.opLinearEquiv addCommMonoid module TensorProduct.addCommMonoid TensorProduct.instModule RingHomCompTriple.ids LinearEquiv.trans TensorProduct.congr LinearEquiv.ofSubmodule' TensorProduct.comm	—	TensorProduct.ext' IsScalarTower.right RingHomInvPair.ids RingHomCompTriple.ids
mulMap_range 📖	mathematical	—	LinearMap.range TensorProduct Submodule CommSemiring.toSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring Algebra.toModule SetLike.instMembership setLike addCommMonoid module TensorProduct.addCommMonoid TensorProduct.instModule RingHom.id RingHomSurjective.ids mulMap mul IsScalarTower.right	—	le_antisymm RingHomSurjective.ids IsScalarTower.right TensorProduct.induction_on map_zero AddMonoidHomClass.toZeroHomClass DistribMulActionSemiHomClass.toAddMonoidHomClass SemilinearMapClass.distribMulActionSemiHomClass LinearMap.semilinearMapClass ZeroMemClass.zero_mem AddSubmonoidClass.toZeroMemClass addSubmonoidClass mul_mem_mul map_add SemilinearMapClass.toAddHomClass AddMemClass.add_mem AddSubmonoidClass.toAddMemClass mul_le
mulMap_tmul 📖	mathematical	—	DFunLike.coe LinearMap CommSemiring.toSemiring RingHom.id Semiring.toNonAssocSemiring TensorProduct Submodule NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Algebra.toModule SetLike.instMembership setLike addCommMonoid module TensorProduct.addCommMonoid TensorProduct.instModule LinearMap.instFunLike mulMap TensorProduct.tmul Distrib.toMul NonUnitalNonAssocSemiring.toDistrib	—	—
mulRightMap_eq_mulMap_comp 📖	mathematical	—	mulRightMap CommSemiring.toSemiring Algebra.toModule smulCommClass_self CommSemiring.toCommMonoid DistribMulAction.toMulAction CommMonoid.toMonoid AddCommMonoid.toAddMonoid NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring Module.toDistribMulAction IsScalarTower.right LinearMap.comp Finsupp Submodule SetLike.instMembership setLike AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass addCommMonoid TensorProduct module Finsupp.instAddCommMonoid TensorProduct.addCommMonoid Finsupp.module TensorProduct.instModule RingHom.id RingHomCompTriple.ids mulMap MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass Semiring.toModule LinearMap.lTensor Finsupp.linearCombination LinearEquiv.toLinearMap RingHomInvPair.ids TensorProduct.leftModule IsScalarTower.to_smulCommClass Algebra.id isScalarTower' Algebra.toSMul SemigroupAction.toSMul Monoid.toSemigroup MonoidWithZero.toMonoid Semiring.toMonoidWithZero MulAction.toSemigroupAction IsScalarTower.left LinearEquiv.symm TensorProduct.finsuppScalarRight	—	Finsupp.lhom_ext' smulCommClass_self IsScalarTower.right RingHomCompTriple.ids RingHomInvPair.ids IsScalarTower.to_smulCommClass isScalarTower' IsScalarTower.left LinearMap.ext mulRightMap_apply_single TensorProduct.finsuppScalarRight_symm_apply_single Finsupp.linearCombination_single one_smul
rTensorOne'_tmul 📖	mathematical	—	DFunLike.coe LinearMap CommSemiring.toSemiring RingHom.id Semiring.toNonAssocSemiring TensorProduct Submodule NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Algebra.toModule SetLike.instMembership setLike Subalgebra Subalgebra.instSetLike Bot.bot OrderBot.toBot Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder Lattice.toSemilatticeSup CompleteLattice.toLattice Algebra.instCompleteLatticeSubalgebra BoundedOrder.toOrderBot CompleteLattice.toBoundedOrder addCommMonoid Subalgebra.toSemiring module Subalgebra.instModuleSubtypeMem TensorProduct.addCommMonoid TensorProduct.instModule LinearMap.instFunLike rTensorOne' TensorProduct.tmul RingHom RingHom.instFunLike algebraMap Subalgebra.algebra smul Algebra.toSMul Algebra.id IsScalarTower.left MonoidWithZero.toMonoid Semiring.toMonoidWithZero DistribMulAction.toMulAction AddCommMonoid.toAddMonoid Module.toDistribMulAction	—	Subtype.val_injective IsScalarTower.left Algebra.smul_def Algebra.commutes mulMap_tmul
rTensorOne'_tmul_one 📖	mathematical	—	DFunLike.coe LinearMap CommSemiring.toSemiring RingHom.id Semiring.toNonAssocSemiring TensorProduct Submodule NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Algebra.toModule SetLike.instMembership setLike Subalgebra Subalgebra.instSetLike Bot.bot OrderBot.toBot Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder Lattice.toSemilatticeSup CompleteLattice.toLattice Algebra.instCompleteLatticeSubalgebra BoundedOrder.toOrderBot CompleteLattice.toBoundedOrder addCommMonoid Subalgebra.toSemiring module Subalgebra.instModuleSubtypeMem TensorProduct.addCommMonoid TensorProduct.instModule LinearMap.instFunLike rTensorOne' TensorProduct.tmul OneMemClass.one AddMonoidWithOne.toOne AddCommMonoidWithOne.toAddMonoidWithOne NonAssocSemiring.toAddCommMonoidWithOne AddSubmonoidWithOneClass.toOneMemClass SubsemiringClass.addSubmonoidWithOneClass Subalgebra.instSubsemiringClass	—	IsScalarTower.left AddSubmonoidWithOneClass.toOneMemClass SubsemiringClass.addSubmonoidWithOneClass Subalgebra.instSubsemiringClass map_one MonoidHomClass.toOneHomClass MonoidWithZeroHomClass.toMonoidHomClass RingHomClass.toMonoidWithZeroHomClass RingHom.instRingHomClass one_smul rTensorOne'_tmul
rTensorOne_symm_apply 📖	mathematical	—	DFunLike.coe LinearEquiv CommSemiring.toSemiring RingHom.id Semiring.toNonAssocSemiring RingHomInvPair.ids Submodule NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Algebra.toModule SetLike.instMembership setLike TensorProduct Subalgebra Subalgebra.instSetLike Bot.bot OrderBot.toBot Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder Lattice.toSemilatticeSup CompleteLattice.toLattice Algebra.instCompleteLatticeSubalgebra BoundedOrder.toOrderBot CompleteLattice.toBoundedOrder addCommMonoid Subalgebra.toSemiring module Subalgebra.instModuleSubtypeMem TensorProduct.addCommMonoid TensorProduct.instModule EquivLike.toFunLike DFinsupp.instEquivLikeLinearEquiv LinearEquiv.symm rTensorOne TensorProduct.tmul OneMemClass.one AddMonoidWithOne.toOne AddCommMonoidWithOne.toAddMonoidWithOne NonAssocSemiring.toAddCommMonoidWithOne AddSubmonoidWithOneClass.toOneMemClass SubsemiringClass.addSubmonoidWithOneClass Subalgebra.instSubsemiringClass	—	RingHomInvPair.ids
rTensorOne_tmul 📖	mathematical	—	DFunLike.coe LinearEquiv CommSemiring.toSemiring RingHom.id Semiring.toNonAssocSemiring RingHomInvPair.ids TensorProduct Submodule NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Algebra.toModule SetLike.instMembership setLike Subalgebra Subalgebra.instSetLike Bot.bot OrderBot.toBot Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder Lattice.toSemilatticeSup CompleteLattice.toLattice Algebra.instCompleteLatticeSubalgebra BoundedOrder.toOrderBot CompleteLattice.toBoundedOrder addCommMonoid Subalgebra.toSemiring module Subalgebra.instModuleSubtypeMem TensorProduct.addCommMonoid TensorProduct.instModule EquivLike.toFunLike DFinsupp.instEquivLikeLinearEquiv rTensorOne TensorProduct.tmul RingHom RingHom.instFunLike algebraMap Subalgebra.algebra smul Algebra.toSMul Algebra.id IsScalarTower.left MonoidWithZero.toMonoid Semiring.toMonoidWithZero DistribMulAction.toMulAction AddCommMonoid.toAddMonoid Module.toDistribMulAction	—	rTensorOne'_tmul
rTensorOne_tmul_one 📖	mathematical	—	DFunLike.coe LinearEquiv CommSemiring.toSemiring RingHom.id Semiring.toNonAssocSemiring RingHomInvPair.ids TensorProduct Submodule NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Algebra.toModule SetLike.instMembership setLike Subalgebra Subalgebra.instSetLike Bot.bot OrderBot.toBot Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder Lattice.toSemilatticeSup CompleteLattice.toLattice Algebra.instCompleteLatticeSubalgebra BoundedOrder.toOrderBot CompleteLattice.toBoundedOrder addCommMonoid Subalgebra.toSemiring module Subalgebra.instModuleSubtypeMem TensorProduct.addCommMonoid TensorProduct.instModule EquivLike.toFunLike DFinsupp.instEquivLikeLinearEquiv rTensorOne TensorProduct.tmul OneMemClass.one AddMonoidWithOne.toOne AddCommMonoidWithOne.toAddMonoidWithOne NonAssocSemiring.toAddCommMonoidWithOne AddSubmonoidWithOneClass.toOneMemClass SubsemiringClass.addSubmonoidWithOneClass Subalgebra.instSubsemiringClass	—	rTensorOne'_tmul_one
val_mulMap'_tmul 📖	mathematical	—	Submodule CommSemiring.toSemiring NonUnitalNonAssocSemiring.toAddCommMonoid NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring Algebra.toModule SetLike.instMembership setLike mul IsScalarTower.right DFunLike.coe LinearMap RingHom.id TensorProduct addCommMonoid module TensorProduct.addCommMonoid TensorProduct.instModule LinearMap.instFunLike mulMap' TensorProduct.tmul Distrib.toMul NonUnitalNonAssocSemiring.toDistrib	—	IsScalarTower.right

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