simp only [add_assoc, add_left_cancel_iff]
case left
Q : Type u_2
K : Type u_1
inst : AddGroup Q
inst_1 : AddCommGroup K
c : Q → Q → K
ccl : Cocycle c
k : K
q : Q
k' : K
q' : Q
k'' : K
q'' : Q
⊢ k + ↑(Cocycle.α c q) k' + c q q' + ↑(Cocycle.α c q) (↑(Cocycle.α c q') k'') + c (q + q') q'' =
    k + (↑(Cocycle.α c q) k' + ↑(Cocycle.α c q) (↑(Cocycle.α c q') k'') + ↑(Cocycle.α c q) (c q' q'')) + c q (q' + q'')
case left
Q : Type u_2
K : Type u_1
inst : AddGroup Q
inst_1 : AddCommGroup K
c : Q → Q → K
ccl : Cocycle c
k : K
q : Q
k' : K
q' : Q
k'' : K
q'' : Q
⊢ c q q' + (↑(Cocycle.α c q) (↑(Cocycle.α c q') k'') + c (q + q') q'') =
    ↑(Cocycle.α c q) (↑(Cocycle.α c q') k'') + (↑(Cocycle.α c q) (c q' q'') + c q (q' + q''))