theorem :: ewhileUsedF:
  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 Lm4
    .= UsedI*Loc (a =0_goto 3 ";"
         Goto  (card IG + 1) ";" (I ';' goto  0)) \/ {} 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;
