obtain ⟨a, b, c, d, ha, hb, hc, hd, rfl⟩ := h
s : ℝ
h : ∃ a b c d, 0 < a ∧ 0 < b ∧ 0 < c ∧ 0 < d ∧ s = a / (a + b + d) + b / (a + b + c) + c / (b + c + d) + d / (a + c + d)
⊢ 1 < s ∧ s < 2
case intro.intro.intro.intro.intro.intro.intro.intro
a b c d : ℝ
ha : 0 < a
hb : 0 < b
hc : 0 < c
hd : 0 < d
⊢ 1 < a / (a + b + d) + b / (a + b + c) + c / (b + c + d) + d / (a + c + d) ∧
    a / (a + b + d) + b / (a + b + c) + c / (b + c + d) + d / (a + c + d) < 2