Mathlib Map

Theorems · Theorem · linear algebra

Module.IsReflexive.of_isPerfPair

∀ {R : Type u_1} {M : Type u_3} {N : Type u_5} [inst : AddCommGroup M] [inst_1 : AddCommGroup N] [inst_2 : CommRing R]
  [inst_3 : Module R M] [inst_4 : Module R N] (p : M →ₗ[R] N →ₗ[R] R) [p.IsPerfPair], Module.IsReflexive R M
Defined in
Mathlib.LinearAlgebra.PerfectPairing.Basic
Cited by
29 results in Mathlib
Foundations
Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommGroupAddCommGroupCommRingModuleModuleLinearMap.IsPerfPair

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

RootPairing.root_sub_root_mem_of_pairingIn_pos · cited by 7RootPairing.root_sub_root…RootPairing.pairingIn_pairingIn_mem_set_of_isCrystal_of_isRed · cited by 6RootPairing.pairingIn_pai…RootPairing.disjoint_rootSpan_ker_rootForm · cited by 5RootPairing.disjoint_root…RootPairing.setOfPred_root_add_zsmul_eq_Icc_of_linearIndependent · cited by 5RootPairing.setOfPred_roo…RootPairing.isCompl_rootSpan_ker_rootForm · cited by 4RootPairing.isCompl_rootS…RootPairing.pairing_eq_zero_iff' · cited by 3RootPairing.pairing_eq_ze…RootPairing.linearIndependent_of_add_mem_range_root' · cited by 3RootPairing.linearIndepen…RootPairing.Base.root_sub_root_mem_of_mem_of_mem · cited by 3Base.root_sub_root_mem_of…RootPairing.pairingIn_pairingIn_mem_set_of_isCrystal_of_isRed' · cited by 2RootPairing.pairingIn_pai…RootPairing.EmbeddedG2.isOrthogonal_short_and_long · cited by 2EmbeddedG2.isOrthogonal_s…RootPairing.finrank_range_polarization_eq_finrank_span_coroot · cited by 2RootPairing.finrank_range…RootPairing.ne_neg · cited by 2RootPairing.ne_negRootPairing.GeckConstruction.isNilpotent_e · cited by 2GeckConstruction.isNilpot…RootPairing.chainBotCoeff_if_one_zero · cited by 2RootPairing.chainBotCoeff…RootPairing.coxeterWeight_zero_iff_isOrthogonal · cited by 1RootPairing.coxeterWeight…DFunLike.coe · cited by 62936DFunLike.coeModule · cited by 20661ModuleRingHom.id · cited by 18349RingHom.idCommRing · cited by 17173CommRingAddCommGroup · cited by 12871AddCommGroupLinearMap · cited by 10215LinearMapLinearEquiv.symm · cited by 1461LinearEquiv.symmFunction.Bijective · cited by 863Function.BijectiveLinearMap.ext · cited by 844LinearMap.extModule.Dual · cited by 583Module.DualLinearEquiv.trans · cited by 298LinearEquiv.transLinearMap.flip · cited by 193LinearMap.flipModule.IsReflexive · cited by 58Module.IsReflexiveModule.Dual.eval · cited by 52Dual.evalLinearMap.toPerfPair · cited by 46LinearMap.toPerfPairIsReflexive.of_isPerfPairCITED BYCITES

Cites19

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by29

Results whose statement or proof uses this declaration.