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

Delete lemmas.lean

Browse source
This commit is contained in:
jstoobysmith 2024-08-19 06:52:40 -04:00
parent aad05f758f
commit 88ff4a99d5
1 changed files with 0 additions and 32 deletions
Download patch file Download diff file Expand all files Collapse all files

32
HepLean/SpaceTime/LorentzTensor/EinsteinNotation/lemmas.lean
View file

@ -1,32 +0,0 @@
/-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
import HepLean.SpaceTime.LorentzTensor.EinsteinNotation.IndexNotation
/-!
# Lemmas regarding Einstein tensors
-/
namespace einsteinTensor
open einsteinTensorColor
open IndexNotation IndexString
open TensorStructure TensorIndex
variable {R : Type} [CommSemiring R] {n m : ℕ}
/-lemma swap_eq_transpose (T : (einsteinTensor R n).Tensor ![Unit.unit, Unit.unit]) :
(T|"ᵢ₁ᵢ₂") ≈ ((toMatrix.symm (toMatrix T).transpose)|"ᵢ₂ᵢ₁") := by
apply And.intro
· apply And.intro
simp only [toTensorColor_eq, indexNotation_eq_color, ColorIndexList.contr, fromIndexStringColor,
mkDualMap, decidableEq_eq_color]
decide
simp only [toTensorColor_eq, indexNotation_eq_color, ColorIndexList.contr, fromIndexStringColor,
mkDualMap, decidableEq_eq_color, ColorIndexList.colorMap']
decide
intro h -/
end einsteinTensor