| import OAI.AlgebraicGeometry.CharacterVarieties.Frames.Mirror | |
| namespace OAI | |
| noncomputable section | |
| namespace IntegralCharacterVarieties.OccurrenceIncidence.VertexTable.LocalRanks | |
| open scoped Classical Matrix | |
| variable {R : Type} [CommRing R] {k : Kind} {d e : LocalRanks k} | |
| def columnCongr (h : d=e) (p : k.table.Port) : d.Columns p ≃ e.Columns p := | |
| Equiv.sigmaCongr (Equiv.refl _) (fun c => finCongr (congrArg (fun z : LocalRanks k => z.rank p (some c)) h)) | |
| def parentCongr (h : d=e) (p : k.table.Port) : d.Parent p ≃ e.Parent p := | |
| finCongr (congrArg (fun z : LocalRanks k => z.rank p none) h) | |
| lemma transportFrames_reindex (h : d=e) | |
| (f : (p : k.table.Port) → MatrixIso R (d.Columns p) (d.Parent p)) (p : k.table.Port) : | |
| (transportFrames h f p).reindex (columnCongr h p) (parentCongr h p)=f p := by | |
| subst e | |
| have hc : columnCongr (d:=d) rfl p=Equiv.refl _ := Equiv.ext (fun _ => rfl) | |
| have hp : parentCongr (d:=d) rfl p=Equiv.refl _ := by ext i; rfl | |
| rw [hc,hp] | |
| exact MatrixIso.reindex_refl_eq _ | |
| end IntegralCharacterVarieties.OccurrenceIncidence.VertexTable.LocalRanks | |
| end | |
| end OAI | |