feat: make informal_definition and informal_lemma commands (#300)
* make informal_definition and informal_lemma commands * drop the fields "math", "physics", and "proof" from InformalDefinition/InformalLemma and use docstrings instead * render informal docstring in dependency graph
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@ -48,17 +48,19 @@ lemma contractSelfField_equivariant {S : TensorSpecies} {c : S.C} {g : S.G}
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simpa using congrFun (congrArg (fun x => x.hom.toFun)
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((S.contractSelfHom c).comm g)) (ψ ⊗ₜ[S.k] φ)
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informal_lemma contractSelfField_non_degenerate where
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math :≈ "The contraction of two vectors of the same color is non-degenerate.
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I.e. ⟪ψ, φ⟫ₜₛ = 0 for all φ implies ψ = 0."
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proof :≈ "The basic idea is that being degenerate contradicts the assumption of having a unit
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in the tensor species."
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deps :≈ [``contractSelfField]
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/-- The contraction of two vectors of the same color is non-degenerate, i.e., `⟪ψ, φ⟫ₜₛ = 0` for all
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`φ` implies `ψ = 0`.
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Proof: the basic idea is that being degenerate contradicts the assumption of having a
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unit in the tensor species.
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-/
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informal_lemma contractSelfField_non_degenerate where
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deps := [``contractSelfField]
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/-- The contraction `⟪ψ, φ⟫ₜₛ` is related to the tensor tree
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`{ψ | μ ⊗ (S.dualRepIsoDiscrete c).hom φ | μ}ᵀ`. -/
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informal_lemma contractSelfField_tensorTree where
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math :≈ "The contraction ⟪ψ, φ⟫ₜₛ is related to the tensor tree
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{ψ | μ ⊗ (S.dualRepIsoDiscrete c).hom φ | μ}ᵀ "
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deps :≈ [``contractSelfField, ``TensorTree]
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deps := [``contractSelfField, ``TensorTree]
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/-!
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