have hE' : w'.E = w.trunc.E
case intro
n d : ℕ
inst✝ : NeZero d
w : Weight n d
hE : E (trunc w) = E w
k : Fin (Nat.succ n)
hk : w k = 0
w' : Weight n d := Function.update (trunc w) k 1
j : Fin (Nat.succ n)
hj : E w < w j
hsum' : Weight.sum w' = Weight.sum (trunc w) + 1
⊢ E w' = E (trunc w) ∧ balanced w' ∧ trunc w ≤ w' ∧ trunc w ≠ w'
case hE'
n d : ℕ
inst✝ : NeZero d
w : Weight n d
hE : E (trunc w) = E w
k : Fin (Nat.succ n)
hk : w k = 0
w' : Weight n d := Function.update (trunc w) k 1
j : Fin (Nat.succ n)
hj : E w < w j
hsum' : Weight.sum w' = Weight.sum (trunc w) + 1
⊢ E w' = E (trunc w)

case intro
n d : ℕ
inst✝ : NeZero d
w : Weight n d
hE : E (trunc w) = E w
k : Fin (Nat.succ n)
hk : w k = 0
w' : Weight n d := Function.update (trunc w) k 1
j : Fin (Nat.succ n)
hj : E w < w j
hsum' : Weight.sum w' = Weight.sum (trunc w) + 1
hE' : E w' = E (trunc w)
⊢ E w' = E (trunc w) ∧ balanced w' ∧ trunc w ≤ w' ∧ trunc w ≠ w'