reserve k,n,m,l,p for Nat;
reserve n0,m0 for non zero Nat;
reserve f for FinSequence;
reserve x,X,Y for set;
reserve f1,f2,f3 for FinSequence of REAL;
reserve n1,n2,m1,m2 for Nat;

theorem
  p is prime implies p |-count(n0 gcd m0) = min(p |-count n0,p |-count m0)
  by Lm1;
