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7f5fab8 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | 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
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