Module: Mathlib.Analysis.Analytic.Composition

Goal state before:
pp: case e'_3
𝕜 : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
H : Type u_5
inst✝⁸ : NontriviallyNormedField 𝕜
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace 𝕜 E
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup G
inst✝² : NormedSpace 𝕜 G
inst✝¹ : NormedAddCommGroup H
inst✝ : NormedSpace 𝕜 H
n✝ n : ℕ
c : Composition n
d : (i : Fin c.length) → Composition (c.blocksFun i)
this : List.map sum (ofFn fun i ↦ (d i).blocks) = c.blocks
e_2✝ :
  ({ blocks := (ofFn fun j ↦ (d j).blocks).flatten, blocks_pos := ⋯, blocks_sum := ⋯ }.gather
        { blocks := ofFn fun j ↦ (d j).length, blocks_pos := ⋯, blocks_sum := ⋯ }).length =
    c.length
⊢ ∀
    (i :
      Fin
        ({ blocks := (ofFn fun j ↦ (d j).blocks).flatten, blocks_pos := ⋯, blocks_sum := ⋯ }.gather
            { blocks := ofFn fun j ↦ (d j).length, blocks_pos := ⋯, blocks_sum := ⋯ }).length),
    ({ blocks := (ofFn fun j ↦ (d j).blocks).flatten, blocks_pos := ⋯, blocks_sum := ⋯ }.sigmaCompositionAux
          { blocks := ofFn fun j ↦ (d j).length, blocks_pos := ⋯, blocks_sum := ⋯ } i).blocks =
      (d ⟨↑i, ⋯⟩).blocks

pp: case e'_3.h
𝕜 : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
H : Type u_5
inst✝⁸ : NontriviallyNormedField 𝕜
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace 𝕜 E
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup G
inst✝² : NormedSpace 𝕜 G
inst✝¹ : NormedAddCommGroup H
inst✝ : NormedSpace 𝕜 H
n✝ n : ℕ
c : Composition n
d : (i : Fin c.length) → Composition (c.blocksFun i)
this : List.map sum (ofFn fun i ↦ (d i).blocks) = c.blocks
e_2✝ :
  ({ blocks := (ofFn fun j ↦ (d j).blocks).flatten, blocks_pos := ⋯, blocks_sum := ⋯ }.gather
        { blocks := ofFn fun j ↦ (d j).length, blocks_pos := ⋯, blocks_sum := ⋯ }).length =
    c.length
⊢ ({ blocks := (ofFn fun j ↦ (d j).blocks).flatten, blocks_pos := ⋯, blocks_sum := ⋯ }.gather
        { blocks := ofFn fun j ↦ (d j).length, blocks_pos := ⋯, blocks_sum := ⋯ }).length =
    c.length

Tactic:
]

Goal state after:
case e'_3
𝕜 : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
H : Type u_5
inst✝⁸ : NontriviallyNormedField 𝕜
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace 𝕜 E
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup G
inst✝² : NormedSpace 𝕜 G
inst✝¹ : NormedAddCommGroup H
inst✝ : NormedSpace 𝕜 H
n✝ n : ℕ
c : Composition n
d : (i : Fin c.length) → Composition (c.blocksFun i)
this : List.map sum (ofFn fun i ↦ (d i).blocks) = c.blocks
e_2✝ :
  ({ blocks := (ofFn fun j ↦ (d j).blocks).flatten, blocks_pos := ⋯, blocks_sum := ⋯ }.gather
        { blocks := ofFn fun j ↦ (d j).length, blocks_pos := ⋯, blocks_sum := ⋯ }).length =
    c.length
⊢ ∀
    (i :
      Fin
        ({ blocks := (ofFn fun j ↦ (d j).blocks).flatten, blocks_pos := ⋯, blocks_sum := ⋯ }.gather
            { blocks := ofFn fun j ↦ (d j).length, blocks_pos := ⋯, blocks_sum := ⋯ }).length),
    ({ blocks := (ofFn fun j ↦ (d j).blocks).flatten, blocks_pos := ⋯, blocks_sum := ⋯ }.sigmaCompositionAux
          { blocks := ofFn fun j ↦ (d j).length, blocks_pos := ⋯, blocks_sum := ⋯ } i).blocks =
      (d ⟨↑i, ⋯⟩).blocks

case e'_3.h
𝕜 : Type u_1
E : Type u_2
F : Type u_3
G : Type u_4
H : Type u_5
inst✝⁸ : NontriviallyNormedField 𝕜
inst✝⁷ : NormedAddCommGroup E
inst✝⁶ : NormedSpace 𝕜 E
inst✝⁵ : NormedAddCommGroup F
inst✝⁴ : NormedSpace 𝕜 F
inst✝³ : NormedAddCommGroup G
inst✝² : NormedSpace 𝕜 G
inst✝¹ : NormedAddCommGroup H
inst✝ : NormedSpace 𝕜 H
n✝ n : ℕ
c : Composition n
d : (i : Fin c.length) → Composition (c.blocksFun i)
this : List.map sum (ofFn fun i ↦ (d i).blocks) = c.blocks
e_2✝ :
  ({ blocks := (ofFn fun j ↦ (d j).blocks).flatten, blocks_pos := ⋯, blocks_sum := ⋯ }.gather
        { blocks := ofFn fun j ↦ (d j).length, blocks_pos := ⋯, blocks_sum := ⋯ }).length =
    c.length
⊢ ({ blocks := (ofFn fun j ↦ (d j).blocks).flatten, blocks_pos := ⋯, blocks_sum := ⋯ }.gather
        { blocks := ofFn fun j ↦ (d j).length, blocks_pos := ⋯, blocks_sum := ⋯ }).length =
    c.length