Theorem: MyNat.add_comm (MIL/C05_Elementary_Number_Theory/S02_Induction_and_Recursion.lean)

State before:
m n : MyNat
⊢ m.add n = n.add m
Tactic:
induction' n with n ih
State after:
case zero
m : MyNat
⊢ m.add zero = zero.add m

case succ
m n : MyNat
ih : m.add n = n.add m
⊢ m.add n.succ = n.succ.add m

State before:
case succ
m n : MyNat
ih : m.add n = n.add m
⊢ m.add n.succ = n.succ.add m
Tactic:
rw [add, succ_add, ih]
State after:
no goals

State before:
case zero
m : MyNat
⊢ m.add zero = zero.add m
Tactic:
rw [zero_add]
State after:
case zero
m : MyNat
⊢ m.add zero = m

State before:
case zero
m : MyNat
⊢ m.add zero = m
Tactic:
rfl
State after:
no goals