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feat: make informal_definition and informal_lemma commands (#300)

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* 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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KUO-TSAN HSU (Gordon) 2025-02-02 03:17:17 +08:00 • committed by GitHub
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25
HepLean/Tensors/TensorSpecies/DualRepIso.lean
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@ -241,27 +241,28 @@ def dualRepIsoDiscrete (c : S.C) : S.FD.obj (Discrete.mk c) ≅ S.FD.obj (Discre
ext x
exact S.fromDualRep_toDualRep_eq_self c x
/-- Given a `i : Fin n` the isomorphism between `S.F.obj (OverColor.mk c)` and
`S.F.obj (OverColor.mk (Function.update c i (S.τ (c i))))` induced by `dualRepIsoDiscrete` acting on
the `i`-th component of the color.
-/
informal_definition dualRepIso where
math :≈ "Given a `i : Fin n` the isomorphism between `S.F.obj (OverColor.mk c)` and
`S.F.obj (OverColor.mk (Function.update c i (S.τ (c i))))` induced by `dualRepIsoDiscrete`
acting on the `i`-th component of the color."
deps :≈ [``dualRepIsoDiscrete]
deps := [``dualRepIsoDiscrete]
/-- Acting with `dualRepIso` on the fst component of a `unitTensor` returns a metric. -/
informal_lemma dualRepIso_unitTensor_fst where
math :≈ "Acting with `dualRepIso` on the fst component of a `unitTensor` returns a metric."
deps :≈ [``dualRepIso, ``unitTensor, ``metricTensor]
deps := [``dualRepIso, ``unitTensor, ``metricTensor]
/-- Acting with `dualRepIso` on the snd component of a `unitTensor` returns a metric. -/
informal_lemma dualRepIso_unitTensor_snd where
math :≈ "Acting with `dualRepIso` on the snd component of a `unitTensor` returns a metric."
deps :≈ [``dualRepIso, ``unitTensor, ``metricTensor]
deps := [``dualRepIso, ``unitTensor, ``metricTensor]
/-- Acting with `dualRepIso` on the fst component of a `metricTensor` returns a unitTensor. -/
informal_lemma dualRepIso_metricTensor_fst where
math :≈ "Acting with `dualRepIso` on the fst component of a `metricTensor` returns a unitTensor."
deps :≈ [``dualRepIso, ``unitTensor, ``metricTensor]
deps := [``dualRepIso, ``unitTensor, ``metricTensor]
/-- Acting with `dualRepIso` on the snd component of a `metricTensor` returns a unitTensor. -/
informal_lemma dualRepIso_metricTensor_snd where
math :≈ "Acting with `dualRepIso` on the snd component of a `metricTensor` returns a unitTensor."
deps :≈ [``dualRepIso, ``unitTensor, ``metricTensor]
deps := [``dualRepIso, ``unitTensor, ``metricTensor]
end TensorSpecies