Define successor, addition, multiplication, zero test, subtraction, predecessor, equality for church numerals?

Church numerals:

• Successor:

  $\text{succ}=\lambda c.\lambda a.\lambda z.a(caz)$.

• Addition:

  $\text{plus}=\lambda m.\lambda n.\lambda a.\lambda z.(ma(naz))$.

• Multiplication:

  $\text{time}=\lambda m.\lambda n.m\text{plus}n$.

• Zero test:

  $\text{iszero}=\lambda c.c(\lambda \_.\text{fls})\text{tru}$

• Predecessor:

  $\text{pred}=\lambda c.\text{fst}(c(\lambda p.\text{pair}(\text{snd}p)(\text{succ}(\text{snd}p)))(\text{pair}{c}_0{c}_0))$

• Subtraction:

  $\text{sub}=\lambda m.\lambda n.n\text{pred}m$.

• Equality:

  $\text{eq}=\lambda m.\lambda n.(\text{and}(\text{iszero}(\text{sub}mn))(\text{iszero}(\text{sub}nm)))$