text: We define the reverse fnction as\nreverse(x.a)=a.x where a belongs to the alphabet set.\nWe prove by induction that \nreverse(xy) = reverse(y). reverse(x)\nBasis: \nlet y = L(lambda the empty string)\nreverse(xy)=reverse(x.L)\n=L.reverse(x)\n=reverse(L).reverse(x)\n\nInduction step:\nLet the induction hypothesis is \nreverse(xz) = reverse(z).reverse(x)\nNow let y = z.a where a belongs to alphabet set.\nSo y>z;\nSo from defination reverse(y)=reverse(z.a)\n=a.reverse(z)....(1)\nNow reverse(xy)=reverse(x.(z.a))\nreverse((x.z).a)=a.reverse(x.z)\n=a.reverse(z).reverse(x)\n[from induction Hypothesis.]\n=reverse(y).reverse(x)[from 1]\nHence proved..