theorem extracted_formal_statement_81 (x : ℝ) (xpos : 0 < x) (h_original_goal : x.sign * |x| = x) : 1 * |x| = x := sorry

State before:
case pos
x : ℝ
xpos : 0 < x
⊢ x.sign * |x| = x

Tactic: rw [Real.sign_of_pos xpos]

State after:
[case pos
 x : ℝ
 xpos : 0 < x
 ⊢ 1 * |x| = x]

Relevant lemmas:
Real.sign_of_pos : ∀ {r : ℝ}, 0 < r → r.sign = 1