
theorem cz2:
the carrier of Z/2 = { 0.(Z/2), 1.(Z/2) }
proof
H: INT.Ring(2) =
    doubleLoopStr(#Segm(2),addint(2),multint(2),In(1,Segm(2)),In(0,Segm(2))#)
    by INT_3:def 12;
I: In(1,Segm(2)) = 1 & In(0,Segm(2))  = 0 by NAT_1:44,SUBSET_1:def 8;
A: now let o be object;
   assume A1: o in the carrier of Z/2;
   then reconsider k = o as Nat by H;
   per cases by H,A1,NAT_1:44,NAT_1:23;
   suppose k = 0;
     hence o in { 0.(Z/2), 1.(Z/2) } by I,H,TARSKI:def 2;
     end;
   suppose k = 1;
     hence o in { 0.(Z/2), 1.(Z/2) } by I,H,TARSKI:def 2;
     end;
   end;
for o being object holds o in { 0.(Z/2), 1.(Z/2) }
  implies o in the carrier of Z/2;
hence thesis by A,TARSKI:2;
end;
