reserve s for non empty typealg,
  T,X,Y,T9,X9,Y9 for FinSequence of s,
  x,y,z,y9,z9 for type of s;
reserve Tr for PreProof of s;
reserve p for Proof of s,
  v for Element of dom p;
reserve A for non empty set,
  a,a1,a2,b for Element of A*;
reserve s for non empty typestr,
  x for type of s;
reserve s for SynTypes_Calculus,
  T,X,Y for FinSequence of s,
  x,y,z for type of s;

theorem
  <*>the carrier of s ==>. x implies
  <*>the carrier of s ==>. y/"(y/"x) & <*>the carrier of s ==>. (x\y)\y
proof
A1: <*y*> ==>. y by Def18;
  then
A2: e(s)^<*y*> ==>. y by FINSEQ_1:34;
A3: <*y*>^e(s) ==>. y by A1,FINSEQ_1:34;
  assume
A4: e(s) ==>. x;
  then
A5: e(s)^<*y/"x*>^e(s) ==>. y by A2,Lm2;
A6: e(s)^<*x\y*>^e(s) ==>. y by A3,A4,Lm6;
A7: e(s)^<*y/"x*> ==>. y by A5,FINSEQ_1:34;
  <*x\y*>^e(s) ==>. y by A6,FINSEQ_1:34;
  hence thesis by A7,Def18;
end;
