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theorem proved term proof

cos_initials

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formal statement (Lean)

 130theorem cos_initials : Real.cos 0 = 1 ∧ deriv (fun x => Real.cos x) 0 = 0 := by

proof body

Term-mode proof.

 131  constructor
 132  · exact Real.cos_zero
 133  · rw [Real.deriv_cos]
 134    simp [Real.sin_zero]
 135
 136/-- **Theorem (ODE Cos Uniqueness)**: The unique solution to H'' = -H with H(0) = 1, H'(0) = 0 is cos. -/

depends on (6)

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