Delta Contr₂ unit
SUSY.N1.deltaContr₂_unit
Plain-language statement
The snake identity (two-module, contr_unit law): contracting x ∈ M into the M-leg of deltaCap₂ b' b ∈ N ⊗ M returns x.
Exact Lean statement
lemma deltaContr₂_unit (b : Basis ι ℂ M) (b' : Basis ι ℂ N) (x : M) :
(TensorProduct.lid ℂ M) ((deltaContr₂ b b').rTensor M
((TensorProduct.assoc ℂ M N M).symm
(x ⊗ₜ[ℂ] LinearMap.toSpanSingleton ℂ _ (deltaCap₂ b' b) 1))) = xFormal artifact
Lean source
lemma deltaContr₂_unit (b : Basis ι ℂ M) (b' : Basis ι ℂ N) (x : M) : (TensorProduct.lid ℂ M) ((deltaContr₂ b b').rTensor M ((TensorProduct.assoc ℂ M N M).symm (x ⊗ₜ[ℂ] LinearMap.toSpanSingleton ℂ _ (deltaCap₂ b' b) 1))) = x := by rw [LinearMap.toSpanSingleton_apply_one, deltaCap₂, TensorProduct.tmul_sum, map_sum, map_sum, map_sum] conv_rhs => rw [← b.sum_equivFun x] refine Finset.sum_congr rfl fun I _ => ?_ rw [TensorProduct.assoc_symm_tmul, LinearMap.rTensor_tmul, TensorProduct.lid_tmul, deltaContr₂_tmul_basis]- Project
- Physlib
- License
- Apache-2.0
- Commit
- dd43e9e65791
- Source
- Physlib/Particles/SuperSymmetry/N1/Basic.lean:283-292
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