Use Applied Lambda Calculus rules to give proofs of

a) Given (true, 1) prove that (true, 1).fst results in a Boolean type and (true 1).snd results in a Natural Number type b) Given {succ 4, if false then true else false}.fst, prove this results in a Natural Number type. a) Given (true, 1) prove that (true, 1).fst results in a Boolean type and (true 1).snd results in a Natural Number type b) Given {succ 4, if false then true else false}.fst, prove this results in a Natural Number type