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import NNG.Metadata
import NNG.MyNat.Addition
open MyNat
theorem MyNat.zero_add (n : ℕ) : 0 + n = n := by
induction n with n hn
· rw [add_zero]
rfl
· rw [add_succ]
rw [hn]
rfl
theorem MyNat.add_assoc (a b c : ℕ) : (a + b) + c = a + (b + c) := by
induction c with c hc
· rw [add_zero]
rw [add_zero]
rfl
· rw [add_succ]
rw [add_succ]
rw [add_succ]
rw [hc]
rfl
theorem MyNat.succ_add (a b : ℕ) : succ a + b = succ (a + b) := by
induction b with d hd
· rw [add_zero]
rfl
· rw [add_succ]
rw [hd]
rw [add_succ]
rfl
theorem MyNat.add_comm (a b : ℕ) : a + b = b + a := by