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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33 changed files with 666 additions and 1089 deletions
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@ -80,15 +80,19 @@ lemma tensorNode_coBispinorDown (p : complexCo) :
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-/
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informal_lemma contrBispinorUp_eq_metric_contr_contrBispinorDown where
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math :≈ "{contrBispinorUp p | α β = εL | α α' ⊗ εR | β β'⊗ contrBispinorDown p | α' β' }ᵀ"
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proof :≈ "Expand `contrBispinorDown` and use fact that metrics contract to the identity."
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deps :≈ [``contrBispinorUp, ``contrBispinorDown, ``leftMetric, ``rightMetric]
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/-- `{contrBispinorUp p | α β = εL | α α' ⊗ εR | β β'⊗ contrBispinorDown p | α' β' }ᵀ`.
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Proof: expand `contrBispinorDown` and use fact that metrics contract to the identity.
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-/
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informal_lemma contrBispinorUp_eq_metric_contr_contrBispinorDown where
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deps := [``contrBispinorUp, ``contrBispinorDown, ``leftMetric, ``rightMetric]
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/-- `{coBispinorUp p | α β = εL | α α' ⊗ εR | β β'⊗ coBispinorDown p | α' β' }ᵀ`.
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proof: expand `coBispinorDown` and use fact that metrics contract to the identity.
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-/
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informal_lemma coBispinorUp_eq_metric_contr_coBispinorDown where
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math :≈ "{coBispinorUp p | α β = εL | α α' ⊗ εR | β β'⊗ coBispinorDown p | α' β' }ᵀ"
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proof :≈ "Expand `coBispinorDown` and use fact that metrics contract to the identity."
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deps :≈ [``coBispinorUp, ``coBispinorDown, ``leftMetric, ``rightMetric]
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deps := [``coBispinorUp, ``coBispinorDown, ``leftMetric, ``rightMetric]
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lemma contrBispinorDown_expand (p : complexContr) :
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{contrBispinorDown p | α β}ᵀ.tensor =
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@ -31,29 +31,29 @@ namespace complexLorentzTensor
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-/
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/-- The covariant metric is symmetric `{η' | μ ν = η' | ν μ}ᵀ`. -/
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informal_lemma coMetric_symm where
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math :≈ "The covariant metric is symmetric {η' | μ ν = η' | ν μ}ᵀ"
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deps :≈ [``coMetric]
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deps := [``coMetric]
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/-- The contravariant metric is symmetric `{η | μ ν = η | ν μ}ᵀ`. -/
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informal_lemma contrMetric_symm where
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math :≈ "The contravariant metric is symmetric {η | μ ν = η | ν μ}ᵀ"
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deps :≈ [``contrMetric]
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deps := [``contrMetric]
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/-- The left metric is antisymmetric `{εL | α α' = - εL | α' α}ᵀ`. -/
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informal_lemma leftMetric_antisymm where
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math :≈ "The left metric is antisymmetric {εL | α α' = - εL | α' α}ᵀ"
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deps :≈ [``leftMetric]
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deps := [``leftMetric]
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/-- The right metric is antisymmetric `{εR | β β' = - εR | β' β}ᵀ`. -/
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informal_lemma rightMetric_antisymm where
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math :≈ "The right metric is antisymmetric {εR | β β' = - εR | β' β}ᵀ"
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deps :≈ [``rightMetric]
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deps := [``rightMetric]
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/-- The alt-left metric is antisymmetric `{εL' | α α' = - εL' | α' α}ᵀ`. -/
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informal_lemma altLeftMetric_antisymm where
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math :≈ "The alt-left metric is antisymmetric {εL' | α α' = - εL' | α' α}ᵀ"
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deps :≈ [``altLeftMetric]
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deps := [``altLeftMetric]
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/-- The alt-right metric is antisymmetric `{εR' | β β' = - εR' | β' β}ᵀ`. -/
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informal_lemma altRightMetric_antisymm where
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math :≈ "The alt-right metric is antisymmetric {εR' | β β' = - εR' | β' β}ᵀ"
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deps :≈ [``altRightMetric]
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deps := [``altRightMetric]
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/-!
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@ -61,35 +61,41 @@ informal_lemma altRightMetric_antisymm where
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-/
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/-- The contraction of the covariant metric with the contravariant metric is the unit
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`{η' | μ ρ ⊗ η | ρ ν = δ' | μ ν}ᵀ`.
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-/
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informal_lemma coMetric_contr_contrMetric where
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math :≈ "The contraction of the covariant metric with the contravariant metric is the unit
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{η' | μ ρ ⊗ η | ρ ν = δ' | μ ν}ᵀ"
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deps :≈ [``coMetric, ``contrMetric, ``coContrUnit]
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deps := [``coMetric, ``contrMetric, ``coContrUnit]
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/-- The contraction of the contravariant metric with the covariant metric is the unit
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`{η | μ ρ ⊗ η' | ρ ν = δ | μ ν}ᵀ`.
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-/
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informal_lemma contrMetric_contr_coMetric where
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math :≈ "The contraction of the contravariant metric with the covariant metric is the unit
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{η | μ ρ ⊗ η' | ρ ν = δ | μ ν}ᵀ"
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deps :≈ [``contrMetric, ``coMetric, ``contrCoUnit]
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deps := [``contrMetric, ``coMetric, ``contrCoUnit]
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/-- The contraction of the left metric with the alt-left metric is the unit
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`{εL | α β ⊗ εL' | β γ = δL | α γ}ᵀ`.
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-/
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informal_lemma leftMetric_contr_altLeftMetric where
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math :≈ "The contraction of the left metric with the alt-left metric is the unit
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{εL | α β ⊗ εL' | β γ = δL | α γ}ᵀ"
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deps :≈ [``leftMetric, ``altLeftMetric, ``leftAltLeftUnit]
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deps := [``leftMetric, ``altLeftMetric, ``leftAltLeftUnit]
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/-- The contraction of the right metric with the alt-right metric is the unit
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`{εR | α β ⊗ εR' | β γ = δR | α γ}ᵀ`.
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-/
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informal_lemma rightMetric_contr_altRightMetric where
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math :≈ "The contraction of the right metric with the alt-right metric is the unit
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{εR | α β ⊗ εR' | β γ = δR | α γ}ᵀ"
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deps :≈ [``rightMetric, ``altRightMetric, ``rightAltRightUnit]
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deps := [``rightMetric, ``altRightMetric, ``rightAltRightUnit]
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/-- The contraction of the alt-left metric with the left metric is the unit
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`{εL' | α β ⊗ εL | β γ = δL' | α γ}ᵀ`.
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-/
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informal_lemma altLeftMetric_contr_leftMetric where
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math :≈ "The contraction of the alt-left metric with the left metric is the unit
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{εL' | α β ⊗ εL | β γ = δL' | α γ}ᵀ"
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deps :≈ [``altLeftMetric, ``leftMetric, ``altLeftLeftUnit]
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deps := [``altLeftMetric, ``leftMetric, ``altLeftLeftUnit]
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/-- The contraction of the alt-right metric with the right metric is the unit
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`{εR' | α β ⊗ εR | β γ = δR' | α γ}ᵀ`.
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-/
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informal_lemma altRightMetric_contr_rightMetric where
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math :≈ "The contraction of the alt-right metric with the right metric is the unit
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{εR' | α β ⊗ εR | β γ = δR' | α γ}ᵀ"
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deps :≈ [``altRightMetric, ``rightMetric, ``altRightRightUnit]
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deps := [``altRightMetric, ``rightMetric, ``altRightRightUnit]
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/-!
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@ -31,32 +31,32 @@ namespace complexLorentzTensor
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-/
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/-- Swapping indices of `coContrUnit` returns `contrCoUnit`: `{δ' | μ ν = δ | ν μ}ᵀ`. -/
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informal_lemma coContrUnit_symm where
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math :≈ "Swapping indices of coContrUnit returns contrCoUnit, i.e. {δ' | μ ν = δ | ν μ}.ᵀ"
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deps :≈ [``coContrUnit, ``contrCoUnit]
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deps := [``coContrUnit, ``contrCoUnit]
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/-- Swapping indices of `contrCoUnit` returns `coContrUnit`: `{δ | μ ν = δ' | ν μ}ᵀ`. -/
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informal_lemma contrCoUnit_symm where
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math :≈ "Swapping indices of contrCoUnit returns coContrUnit, i.e. {δ | μ ν = δ' | ν μ}ᵀ"
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deps :≈ [``contrCoUnit, ``coContrUnit]
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deps := [``contrCoUnit, ``coContrUnit]
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/-- Swapping indices of `altLeftLeftUnit` returns `leftAltLeftUnit`: `{δL' | α α' = δL | α' α}ᵀ`. -/
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informal_lemma altLeftLeftUnit_symm where
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math :≈ "Swapping indices of altLeftLeftUnit returns leftAltLeftUnit, i.e.
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{δL' | α α' = δL | α' α}ᵀ"
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deps :≈ [``altLeftLeftUnit, ``leftAltLeftUnit]
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deps := [``altLeftLeftUnit, ``leftAltLeftUnit]
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/-- Swapping indices of `leftAltLeftUnit` returns `altLeftLeftUnit`: `{δL | α α' = δL' | α' α}ᵀ`. -/
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informal_lemma leftAltLeftUnit_symm where
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math :≈ "Swapping indices of leftAltLeftUnit returns altLeftLeftUnit, i.e.
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{δL | α α' = δL' | α' α}ᵀ"
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deps :≈ [``leftAltLeftUnit, ``altLeftLeftUnit]
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deps := [``leftAltLeftUnit, ``altLeftLeftUnit]
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/-- Swapping indices of `altRightRightUnit` returns `rightAltRightUnit`:
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`{δR' | β β' = δR | β' β}ᵀ`.
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-/
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informal_lemma altRightRightUnit_symm where
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math :≈ "Swapping indices of altRightRightUnit returns rightAltRightUnit, i.e.
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{δR' | β β' = δR | β' β}ᵀ"
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deps :≈ [``altRightRightUnit, ``rightAltRightUnit]
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deps := [``altRightRightUnit, ``rightAltRightUnit]
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/-- Swapping indices of `rightAltRightUnit` returns `altRightRightUnit`:
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`{δR | β β' = δR' | β' β}ᵀ`.
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-/
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informal_lemma rightAltRightUnit_symm where
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math :≈ "Swapping indices of rightAltRightUnit returns altRightRightUnit, i.e.
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{δR | β β' = δR' | β' β}ᵀ"
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deps :≈ [``rightAltRightUnit, ``altRightRightUnit]
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deps := [``rightAltRightUnit, ``altRightRightUnit]
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end complexLorentzTensor
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