Add .gitpod.yml
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.gitpod.yml
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.gitpod.yml
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# This is run when starting a Gitpod workspace on this repository
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image: leanprovercommunity/gitpod4
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vscode:
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extensions:
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- leanprover.lean4 # install the Lean 4 VS Code extension
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tasks:
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- init: |
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elan self update
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lake exe cache get
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@ -52,6 +52,8 @@ lemma coMetric_basis_expand : {η' | μ ν}ᵀ.tensor =
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simp only [Fin.isValue, Lorentz.complexCoBasisFin4, Basis.coe_reindex, Function.comp_apply]
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simp only [Fin.isValue, Lorentz.complexCoBasisFin4, Basis.coe_reindex, Function.comp_apply]
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rfl
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rfl
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/-- Provides the explicit expansion of the co-metric tensor in terms of the basis elements, as
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a tensor tree.-/
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lemma coMetric_basis_expand_tree : {η' | μ ν}ᵀ.tensor =
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lemma coMetric_basis_expand_tree : {η' | μ ν}ᵀ.tensor =
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(TensorTree.add (tensorNode (basisVector ![Color.down, Color.down] (fun _ => 0))) <|
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(TensorTree.add (tensorNode (basisVector ![Color.down, Color.down] (fun _ => 0))) <|
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TensorTree.add (smul (-1) (tensorNode (basisVector ![Color.down, Color.down] (fun _ => 1)))) <|
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TensorTree.add (smul (-1) (tensorNode (basisVector ![Color.down, Color.down] (fun _ => 1)))) <|
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