∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {H : Type u_3} [inst_3 : TopologicalSpace H] {I : ModelWithCorners 𝕜 E H} {M : Type u_4}
  [inst_4 : TopologicalSpace M] [inst_5 : ChartedSpace H M] [inst_6 : IsManifold I 1 M] {E' : Type u_5}
  [inst_7 : NormedAddCommGroup E'] [inst_8 : NormedSpace 𝕜 E'] {H' : Type u_6} [inst_9 : TopologicalSpace H']
  {I' : ModelWithCorners 𝕜 E' H'} {M' : Type u_7} [inst_10 : TopologicalSpace M'] [inst_11 : ChartedSpace H' M']
  [inst_12 : IsManifold I' 1 M'] {N : Type u_8} {f : N → M} {g : N → M'}
  {ϕ : (x : N) → TangentSpace I (f x) →L[𝕜] TangentSpace I' (g x)} {x₀ x : N},
  f x ∈ (chartAt H (f x₀)).source →
    g x ∈ (chartAt H' (g x₀)).source →
      inTangentCoordinates I I' f g ϕ x₀ x =
        (mfderiv% ↑(extChartAt I' (g x₀)) (g x)).comp
          ((ϕ x).comp
            (mfderivWithin (modelWithCornersSelf 𝕜 E) I (↑(extChartAt I (f x₀)).symm) (Set.range ↑I)
              (↑(extChartAt I (f x₀)) (f x))))