apply Nat.le_of_lt_succ (Nat.mod_lt _ (Nat.zero_lt_succ _))
case h₂.h₂.h₂.h.h.a.a.h₂
a b✝ c✝ b c : ℕ
⊢ a % (b + 1) ≤ ?h₂.h₂.h₂.h.h.a.a.d

case h₂.h₂.h₂.h.h.a.a.d
a b✝ c✝ b c : ℕ
⊢ ℕ

case h₂.h₂.h₂.h.h.a
a b✝ c✝ b c : ℕ
⊢ succ ((b + 1) * c + ?h₂.h₂.h₂.h.h.a.a.d) ≤ (b + 1) * (c + 1)
case h₂.h₂.h₂.h.h.a
a b✝ c✝ b c : ℕ
⊢ succ ((b + 1) * c + b) ≤ (b + 1) * (c + 1)