reserve p,p1,p2,h for Instruction-Sequence of SCM+FSA;
reserve k, l, n for Nat,
  j for Integer,
  i,i1 for Instruction of SCM+FSA;
reserve s, s1, s2 for State of SCM+FSA,
  a for read-write Int-Location,
  b for Int-Location,
  I, J for MacroInstruction of SCM+FSA,
  Ig for good MacroInstruction of SCM+FSA,
  i, j, k, m, n for Nat;

theorem Th25:
  UsedI*Loc while>0(b, I) = UsedI*Loc I
proof
  set J = Stop SCM+FSA;
  set a = b;
  set IG = I ';' goto  0;
A1: UsedI*Loc(I ';' goto  0) = UsedI*Loc I by SF_MASTR:67;
  thus UsedI*Loc while>0(a, I) = (UsedI*Loc if>0(a, IG)) by Lm6
    .= UsedI*Loc (a >0_goto 3 ";"
         Goto  (card IG + 1) ";" IG) \/ {} by Th4,SF_MASTR:43
    .= UsedI*Loc (a >0_goto 3 ";"
         Goto  (card IG + 1)) \/ UsedI*Loc I by A1,SF_MASTR:43
    .= UsedInt*Loc (a >0_goto 3) \/
        UsedI*Loc Goto  (card IG + 1) \/ UsedI*Loc I by SF_MASTR:45
    .= UsedInt*Loc (a >0_goto 3) \/ {} \/ UsedI*Loc I by Th6
    .= {} \/ UsedI*Loc I by SF_MASTR:32
    .= UsedI*Loc I;
end;
