constructor
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
case intro.intro.intro.intro.intro.intro.intro.intro.left
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)

case intro.intro.intro.intro.intro.intro.intro.intro.right
a b c d : ℝ
ha : 0 < a
hb : 0 < b
hc : 0 < c
hd : 0 < d
⊢ a / (a + b + d) + b / (a + b + c) + c / (b + c + d) + d / (a + c + d) < 2