DibyashanuPati/PhysLean
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions

refactor: Last batch of multi-goal proofs

Browse source
This commit is contained in:
jstoobysmith 2024-08-21 06:40:58 -04:00
parent b9479c904d
commit c0499483a8
43 changed files with 910 additions and 955 deletions
Download patch file Download diff file Expand all files Collapse all files

5
HepLean/SpaceTime/LorentzTensor/EinsteinNotation/Basic.lean
View file

@ -72,9 +72,8 @@ noncomputable def einsteinTensor (R : Type) [CommSemiring R] (n : ℕ) : TensorS
assoc_tmul, map_tmul, LinearMap.id_coe, id_eq, assoc_symm_tmul, lift.tmul,
Fintype.total_apply, LinearMap.stdBasis_apply', smul_eq_mul, mul_ite, mul_one, mul_zero,
Finset.sum_ite_eq, Finset.mem_univ, ↓reduceIte, lid_tmul, ite_smul, one_smul, zero_smul]
rw [if_neg]
rw [if_neg (id (Ne.symm hi))]
simp only [tmul_zero]
exact id (Ne.symm hi)
namespace einsteinTensor
@ -97,7 +96,7 @@ def toVec : (einsteinTensor R n).Tensor ![Unit.unit] ≃ₗ[R] Fin n → R :=
def toMatrix : (einsteinTensor R n).Tensor ![Unit.unit, Unit.unit] ≃ₗ[R] Matrix (Fin n) (Fin n) R :=
((einsteinTensor R n).mapIso ((Fin.castOrderIso
(by rfl : (Nat.succ 0).succ = Nat.succ 0 + Nat.succ 0)).toEquiv.trans
finSumFinEquiv.symm) (by funext x; fin_cases x; rfl; rfl)).trans <|
finSumFinEquiv.symm) (by funext x; fin_cases x <;> rfl)).trans <|
((einsteinTensor R n).tensoratorEquiv ![0] ![0]).symm.trans <|
(TensorProduct.congr ((PiTensorProduct.subsingletonEquiv 0))
((PiTensorProduct.subsingletonEquiv 0))).trans <|