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Example: Greatest Common Divisor

gcd(x, y) := such z in N: z | x /\  z | y /\  (forall w: (w | x /\  w | y) => w <= z).

fun gcd(x, y) =
  let(m = if(=(x, N0), y, x):
    such(z in nat(N0, m):
      and(divides(z, x), divides(z, y),
        forall(w in nat(+N(z, N1), m):
          or(not(divides(w, x)), not(divides(w, y))))),
      z));

Extremely inefficient way to compute the greatest common divisor.