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theorem proved tactic proof

FApply_square

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formal statement (Lean)

 214theorem FApply_square {n : ℕ}
 215    (lam : ℝ) (hInv : Fin n → Fin n → ℝ) (β : Vec n)
 216    (hμ : mu lam hInv β ≠ 0) (v : Vec n) :
 217    FApply lam hInv β (FApply lam hInv β v) = v := by

proof body

Tactic-mode proof.

 218  ext i
 219  have hPFi : PApply lam hInv β (FApply lam hInv β v) i = PApply lam hInv β v i := by
 220    simpa using congrFun (PApply_FApply lam hInv β hμ v) i
 221  calc
 222    FApply lam hInv β (FApply lam hInv β v) i
 223        = (2 • PApply lam hInv β (FApply lam hInv β v) - FApply lam hInv β v) i := by
 224            simp [FApply]
 225    _ = (2 • PApply lam hInv β v - FApply lam hInv β v) i := by
 226          simp [hPFi]
 227    _ = v i := by
 228          simp [FApply]
 229

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