reserve x,A for set,
  i,j,k,m,n, l, l1, l2 for Nat;
reserve D for non empty set,
  z for Nat;
reserve y for set;

theorem
 for S being standard-ins non empty set
 for T being InsType of S
  ex I being Element of S st InsCode I = T
 proof let S be standard-ins non empty set;
  let T be InsType of S;
   consider y being object such that
A1: [T,y] in proj1 S by XTUPLE_0:def 12;
   consider z being object such that
A2: [[T,y],z] in S by A1,XTUPLE_0:def 12;
   reconsider I = [[T,y],z] as Element of S by A2;
  take I;
  thus InsCode I = T;
 end;
