refactor: Fix problem with elab and do lint
This commit is contained in:
parent
95857993b5
commit
1e8efdb16a
6 changed files with 217 additions and 152 deletions
|
@ -203,7 +203,8 @@ lemma rightAltContraction_hom_tmul (ψ : rightHanded) (φ : altRightHanded) :
|
|||
rfl
|
||||
|
||||
lemma rightAltContraction_basis (i j : Fin 2) :
|
||||
rightAltContraction.hom (rightBasis i ⊗ₜ altRightBasis j) = if i.1 = j.1 then (1 : ℂ) else 0 := by
|
||||
rightAltContraction.hom (rightBasis i ⊗ₜ altRightBasis j) =
|
||||
if i.1 = j.1 then (1 : ℂ) else 0 := by
|
||||
rw [rightAltContraction_hom_tmul]
|
||||
simp only [Action.instMonoidalCategory_tensorUnit_V, rightBasis_toFin2ℂ, altRightBasis_toFin2ℂ,
|
||||
dotProduct_single, mul_one]
|
||||
|
@ -242,7 +243,8 @@ lemma altRightContraction_hom_tmul (φ : altRightHanded) (ψ : rightHanded) :
|
|||
rfl
|
||||
|
||||
lemma altRightContraction_basis (i j : Fin 2) :
|
||||
altRightContraction.hom (altRightBasis i ⊗ₜ rightBasis j) = if i.1 = j.1 then (1 : ℂ) else 0 := by
|
||||
altRightContraction.hom (altRightBasis i ⊗ₜ rightBasis j) =
|
||||
if i.1 = j.1 then (1 : ℂ) else 0 := by
|
||||
rw [altRightContraction_hom_tmul]
|
||||
simp only [Action.instMonoidalCategory_tensorUnit_V, rightBasis_toFin2ℂ, altRightBasis_toFin2ℂ,
|
||||
dotProduct_single, mul_one]
|
||||
|
|
|
@ -125,7 +125,8 @@ def altRightAltRightToMatrix : (altRightHanded ⊗ altRightHanded).V ≃ₗ[ℂ]
|
|||
|
||||
/-- Expanding `altRightAltRightToMatrix` in terms of the standard basis. -/
|
||||
lemma altRightAltRightToMatrix_symm_expand_tmul (M : Matrix (Fin 2) (Fin 2) ℂ) :
|
||||
altRightAltRightToMatrix.symm M = ∑ i, ∑ j, M i j • (altRightBasis i ⊗ₜ[ℂ] altRightBasis j) := by
|
||||
altRightAltRightToMatrix.symm M =
|
||||
∑ i, ∑ j, M i j • (altRightBasis i ⊗ₜ[ℂ] altRightBasis j) := by
|
||||
simp only [Action.instMonoidalCategory_tensorObj_V, altRightAltRightToMatrix,
|
||||
LinearEquiv.trans_symm, LinearEquiv.trans_apply, Basis.repr_symm_apply]
|
||||
rw [Finsupp.linearCombination_apply_of_mem_supported ℂ (s := Finset.univ)]
|
||||
|
|
Loading…
Add table
Add a link
Reference in a new issue