$1.$ Write a lemma called LemProp$1$ that uses level$-1$ induction to prove the property: $42$n $1$ is divisible by $5$ for integers n $0$ If you use properties of exponent arithmetic in the inductive proof then you should use sub$-$lemmas, which may be level $0.$ Write a method that validates the lemma for all n $0.$ You may use any name for the validator. $2.$ Write a second lemma called LemProp$2$ that uses a level$-1$ proof $($any technique used in lectures$)$ to prove the property: if $($m$31)($n $3+1)$ is even then m is odd or n is odd, where m and n are integers Write a method that validates the lemma for all integers m and n$.$ You may use any name for the validator. Submit the file ex$4.$dfy$,$ which should contain the lemmas LemProp$1$ and LemProp$2$ and their corresponding validators.