Contr right Dual Right Unit
Fermion.contr_rightDualRightUnit
Plain-language statement
Contraction on the right with rightDualRightUnit does nothing.
Exact Lean statement
lemma contr_rightDualRightUnit (x : DualRightHandedWeyl) :
(TensorProduct.lid ℂ _ <|
dualRightContraction.toLinearMap.rTensor _ <|
(TensorProduct.assoc ℂ _ _ _).symm <|
x ⊗ₜ[ℂ] (rightDualRightUnit (1 : ℂ))) = xFormal artifact
Lean source
lemma contr_rightDualRightUnit (x : DualRightHandedWeyl) : (TensorProduct.lid ℂ _ <| dualRightContraction.toLinearMap.rTensor _ <| (TensorProduct.assoc ℂ _ _ _).symm <| x ⊗ₜ[ℂ] (rightDualRightUnit (1 : ℂ))) = x := by obtain ⟨c, hc⟩ := (Submodule.mem_span_range_iff_exists_fun ℂ).mp (Basis.mem_span DualRightHandedWeyl.basis x) subst hc simp [- Fintype.sum_sum_type, smul_tmul, dualRightContraction_basis, rightDualRightUnit_apply_one, rightDualRightUnitVal_expand_tmul, add_tmul, tmul_add]- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/Relativity/Fermions/Weyl/Unit.lean:253-262
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