set J = Stop SCM+FSA ;
set G = Goto 0 ;
let a be Int-Location ; :: thesis: for I being Program of SCM+FSA holds
( (card I) + 4 in dom (if>0 a,(I ';' (Goto 0 )),(Stop SCM+FSA )) & (if>0 a,(I ';' (Goto 0 )),(Stop SCM+FSA )) . ((card I) + 4) = goto (0 + ((card I) + 4)) )
let I be Program of SCM+FSA ; :: thesis: ( (card I) + 4 in dom (if>0 a,(I ';' (Goto 0 )),(Stop SCM+FSA )) & (if>0 a,(I ';' (Goto 0 )),(Stop SCM+FSA )) . ((card I) + 4) = goto (0 + ((card I) + 4)) )
set I1 = I ';' (Goto 0 );
set i = a >0_goto ((card (Stop SCM+FSA )) + 3);
set c4 = (card I) + 4;
set Lc4 = (card I) + 4;
set Mi = (((Macro (a >0_goto ((card (Stop SCM+FSA )) + 3))) ';' (Stop SCM+FSA )) ';' (Goto ((card (I ';' (Goto 0 ))) + 1))) ';' I;
x: card (Stop SCM+FSA ) = 1 by COMPOS_1:46;
A1: card ((Goto 0 ) ';' (Stop SCM+FSA )) = (card (Goto 0 )) + (card (Stop SCM+FSA )) by SCMFSA6A:61
.= 1 + 1 by x, SCMFSA8A:29
.= 2 ;
A2: if>0 a,(I ';' (Goto 0 )),(Stop SCM+FSA ) = ((((a >0_goto ((card (Stop SCM+FSA )) + 3)) ';' (Stop SCM+FSA )) ';' (Goto ((card (I ';' (Goto 0 ))) + 1))) ';' (I ';' (Goto 0 ))) ';' (Stop SCM+FSA ) by SCMFSA8B:def 2
.= (((((Macro (a >0_goto ((card (Stop SCM+FSA )) + 3))) ';' (Stop SCM+FSA )) ';' (Goto ((card (I ';' (Goto 0 ))) + 1))) ';' I) ';' (Goto 0 )) ';' (Stop SCM+FSA ) by SCMFSA6A:67
.= ((((Macro (a >0_goto ((card (Stop SCM+FSA )) + 3))) ';' (Stop SCM+FSA )) ';' (Goto ((card (I ';' (Goto 0 ))) + 1))) ';' I) ';' ((Goto 0 ) ';' (Stop SCM+FSA )) by SCMFSA6A:67 ;
then card (if>0 a,(I ';' (Goto 0 )),(Stop SCM+FSA )) = (card ((((Macro (a >0_goto ((card (Stop SCM+FSA )) + 3))) ';' (Stop SCM+FSA )) ';' (Goto ((card (I ';' (Goto 0 ))) + 1))) ';' I)) + (card ((Goto 0 ) ';' (Stop SCM+FSA ))) by SCMFSA6A:61;
then A3: card ((((Macro (a >0_goto ((card (Stop SCM+FSA )) + 3))) ';' (Stop SCM+FSA )) ';' (Goto ((card (I ';' (Goto 0 ))) + 1))) ';' I) = (card (if>0 a,(I ';' (Goto 0 )),(Stop SCM+FSA ))) - (card ((Goto 0 ) ';' (Stop SCM+FSA )))
.= ((card I) + 6) - 2 by A1, SCMFSA_9:2
.= (card I) + 4 ;
then A4: not (card I) + 4 in dom ((((Macro (a >0_goto ((card (Stop SCM+FSA )) + 3))) ';' (Stop SCM+FSA )) ';' (Goto ((card (I ';' (Goto 0 ))) + 1))) ';' I) ;
set GJ = (Goto 0 ) ';' (Stop SCM+FSA );
A5: InsCode (goto 0 ) = 6 by SCMFSA_2:47;
A6: Goto 0 = 0 .--> (goto 0 ) by SCMFSA8A:def 2;
then A7: (Goto 0 ) . 0 = goto 0 by FUNCOP_1:87;
dom (Goto 0 ) = {0 } by A6, FUNCOP_1:19;
then A8: 0 in dom (Goto 0 ) by TARSKI:def 1;
A9: dom (Goto 0 ) c= dom ((Goto 0 ) ';' (Stop SCM+FSA )) by SCMFSA6A:56;
then 0 + ((card I) + 4) in { (il + ((card I) + 4)) where il is Element of NAT : il in dom ((Goto 0 ) ';' (Stop SCM+FSA )) } by A8;
then A10: (card I) + 4 in dom (Shift ((Goto 0 ) ';' (Stop SCM+FSA )),((card I) + 4)) by VALUED_1:def 12;
then A11: (Shift ((Goto 0 ) ';' (Stop SCM+FSA )),((card I) + 4)) /. ((card I) + 4) = (Shift ((Goto 0 ) ';' (Stop SCM+FSA )),((card I) + 4)) . (0 + ((card I) + 4)) by PARTFUN1:def 8
.= ((Goto 0 ) ';' (Stop SCM+FSA )) . 0 by A8, A9, VALUED_1:def 12
.= goto 0 by A8, A7, A5, SCMFSA6A:54, SCMFSA_2:124 ;
x: card (Stop SCM+FSA ) = 1 by COMPOS_1:46;
card (I ';' (Goto 0 )) = (card I) + (card (Goto 0 )) by SCMFSA6A:61
.= (card I) + 1 by SCMFSA8A:29 ;
then ((card (I ';' (Goto 0 ))) + (card (Stop SCM+FSA ))) + 3 = ((card I) + 4) + 1 by x;
then (card I) + 4 < ((card (I ';' (Goto 0 ))) + (card (Stop SCM+FSA ))) + 3 by NAT_1:13;
hence A12: (card I) + 4 in dom (if>0 a,(I ';' (Goto 0 )),(Stop SCM+FSA )) by SCMFSA8C:57; :: thesis: (if>0 a,(I ';' (Goto 0 )),(Stop SCM+FSA )) . ((card I) + 4) = goto (0 + ((card I) + 4))
A13: dom (if>0 a,(I ';' (Goto 0 )),(Stop SCM+FSA )) = (dom (Directed ((((Macro (a >0_goto ((card (Stop SCM+FSA )) + 3))) ';' (Stop SCM+FSA )) ';' (Goto ((card (I ';' (Goto 0 ))) + 1))) ';' I))) \/ (dom (ProgramPart (Relocated ((Goto 0 ) ';' (Stop SCM+FSA )),((card I) + 4)))) by A2, A3, FUNCT_4:def 1;
then dom (if>0 a,(I ';' (Goto 0 )),(Stop SCM+FSA )) = (dom ((((Macro (a >0_goto ((card (Stop SCM+FSA )) + 3))) ';' (Stop SCM+FSA )) ';' (Goto ((card (I ';' (Goto 0 ))) + 1))) ';' I)) \/ (dom (ProgramPart (Relocated ((Goto 0 ) ';' (Stop SCM+FSA )),((card I) + 4)))) by FUNCT_4:105;
then (card I) + 4 in dom (ProgramPart (Relocated ((Goto 0 ) ';' (Stop SCM+FSA )),((card I) + 4))) by A12, A4, XBOOLE_0:def 3;
hence (if>0 a,(I ';' (Goto 0 )),(Stop SCM+FSA )) . ((card I) + 4) = (ProgramPart (Relocated ((Goto 0 ) ';' (Stop SCM+FSA )),((card I) + 4))) . ((card I) + 4) by A12, A2, A3, A13, FUNCT_4:def 1
.= (Reloc (ProgramPart ((Goto 0 ) ';' (Stop SCM+FSA ))),((card I) + 4)) . ((card I) + 4) by AMISTD_2:69
.= (Reloc ((Goto 0 ) ';' (Stop SCM+FSA )),((card I) + 4)) . ((card I) + 4) by RELAT_1:209
.= IncAddr (goto 0 ),((card I) + 4) by A10, A11, SCMFSA_4:24
.= goto (0 + ((card I) + 4)) by SCMFSA_4:14 ;
:: thesis: verum