 reserve i,j,k,k0,m,n,N for Nat;
 reserve x,y for Real;
 reserve p for Prime;
 reserve s for Real_Sequence;

theorem CardSetPrime1:
  p < n implies card SetPrimenumber p + 1 <= card SetPrimenumber n
  proof
    assume p < n; then
    card (SetPrimenumber p \/ {p}) <= card SetPrimenumber n
      by NEWTON:76,NAT_1:43;
    hence thesis by NEWTON:74,CARD_2:41;
  end;
