Mathlib Map

Theorems · Theorem · commutative algebra

LinearEquiv.refl_apply

∀ {R : Type u_1} {M : Type u_7} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (x : M),
  (LinearEquiv.refl R M) x = x
Defined in
Mathlib.Algebra.Module.Equiv.Defs
Cited by
4 results in Mathlib
Foundations
Depth 26 from the axioms · uses propext, Quot.sound
Assumes
SemiringAddCommMonoidModule
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

LinearMap.BilinForm.nondegenerate_congr_iff · cited by 1BilinForm.nondegenerate_c…IsLocalizedModule.map_LocalizedModules · cited by 1IsLocalizedModule.map_Loc…LinearEquiv.lTensor_refl_apply · cited by 0LinearEquiv.lTensor_refl_…LinearEquiv.rTensor_refl_apply · cited by 0LinearEquiv.rTensor_refl_…DFunLike.coe · cited by 62936DFunLike.coeModule · cited by 20661ModuleRingHom.id · cited by 18349RingHom.idSemiring · cited by 13802SemiringAddCommMonoid · cited by 12281AddCommMonoidLinearEquiv · cited by 3317LinearEquivLinearEquiv.refl · cited by 143LinearEquiv.reflLinearEquiv.refl_applyCITED BYCITES

Cites7

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

Cited by4

Results whose statement or proof uses this declaration.