let f be FinSeq-Location ; :: thesis: card (bubble-sort f) = 53
set i1 = (intloc 4) := (intloc 3);
set i2 = SubFrom ((intloc 3),(intloc 0));
set i3 = (intloc 5) := (f,(intloc 3));
set i4 = (intloc 6) := (f,(intloc 4));
set i5 = SubFrom ((intloc 6),(intloc 5));
set i6 = (f,(intloc 3)) := (intloc 6);
set i7 = (f,(intloc 4)) := (intloc 5);
set ifc = if>0 ((intloc 6),((((intloc 6) := (f,(intloc 4))) ";" ((f,(intloc 3)) := (intloc 6))) ";" ((f,(intloc 4)) := (intloc 5))),(Stop SCM+FSA));
set Cif = card (if>0 ((intloc 6),((((intloc 6) := (f,(intloc 4))) ";" ((f,(intloc 3)) := (intloc 6))) ";" ((f,(intloc 4)) := (intloc 5))),(Stop SCM+FSA)));
set body2 = ((((((intloc 4) := (intloc 3)) ";" (SubFrom ((intloc 3),(intloc 0)))) ";" ((intloc 5) := (f,(intloc 3)))) ";" ((intloc 6) := (f,(intloc 4)))) ";" (SubFrom ((intloc 6),(intloc 5)))) ";" (if>0 ((intloc 6),((((intloc 6) := (f,(intloc 4))) ";" ((f,(intloc 3)) := (intloc 6))) ";" ((f,(intloc 4)) := (intloc 5))),(Stop SCM+FSA)));
card (Stop SCM+FSA) = 1 by COMPOS_1:4;
then A1: card (if>0 ((intloc 6),((((intloc 6) := (f,(intloc 4))) ";" ((f,(intloc 3)) := (intloc 6))) ";" ((f,(intloc 4)) := (intloc 5))),(Stop SCM+FSA))) = ((card ((((intloc 6) := (f,(intloc 4))) ";" ((f,(intloc 3)) := (intloc 6))) ";" ((f,(intloc 4)) := (intloc 5)))) + 1) + 4 by SCMFSA8B:12
.= (6 + 1) + 4 by Th15
.= 11 ;
A2: card (((((((intloc 4) := (intloc 3)) ";" (SubFrom ((intloc 3),(intloc 0)))) ";" ((intloc 5) := (f,(intloc 3)))) ";" ((intloc 6) := (f,(intloc 4)))) ";" (SubFrom ((intloc 6),(intloc 5)))) ";" (if>0 ((intloc 6),((((intloc 6) := (f,(intloc 4))) ";" ((f,(intloc 3)) := (intloc 6))) ";" ((f,(intloc 4)) := (intloc 5))),(Stop SCM+FSA)))) = (card ((((((intloc 4) := (intloc 3)) ";" (SubFrom ((intloc 3),(intloc 0)))) ";" ((intloc 5) := (f,(intloc 3)))) ";" ((intloc 6) := (f,(intloc 4)))) ";" (SubFrom ((intloc 6),(intloc 5))))) + (card (if>0 ((intloc 6),((((intloc 6) := (f,(intloc 4))) ";" ((f,(intloc 3)) := (intloc 6))) ";" ((f,(intloc 4)) := (intloc 5))),(Stop SCM+FSA)))) by SCMFSA6A:21
.= (card (((((intloc 4) := (intloc 3)) ";" (SubFrom ((intloc 3),(intloc 0)))) ";" ((intloc 5) := (f,(intloc 3)))) ";" (((intloc 6) := (f,(intloc 4))) ";" (SubFrom ((intloc 6),(intloc 5)))))) + (card (if>0 ((intloc 6),((((intloc 6) := (f,(intloc 4))) ";" ((f,(intloc 3)) := (intloc 6))) ";" ((f,(intloc 4)) := (intloc 5))),(Stop SCM+FSA)))) by SCMFSA6A:28
.= ((card ((((intloc 4) := (intloc 3)) ";" (SubFrom ((intloc 3),(intloc 0)))) ";" ((intloc 5) := (f,(intloc 3))))) + (card (((intloc 6) := (f,(intloc 4))) ";" (SubFrom ((intloc 6),(intloc 5)))))) + (card (if>0 ((intloc 6),((((intloc 6) := (f,(intloc 4))) ";" ((f,(intloc 3)) := (intloc 6))) ";" ((f,(intloc 4)) := (intloc 5))),(Stop SCM+FSA)))) by SCMFSA6A:21
.= (6 + (card (((intloc 6) := (f,(intloc 4))) ";" (SubFrom ((intloc 6),(intloc 5)))))) + (card (if>0 ((intloc 6),((((intloc 6) := (f,(intloc 4))) ";" ((f,(intloc 3)) := (intloc 6))) ";" ((f,(intloc 4)) := (intloc 5))),(Stop SCM+FSA)))) by Th15
.= (6 + 4) + (card (if>0 ((intloc 6),((((intloc 6) := (f,(intloc 4))) ";" ((f,(intloc 3)) := (intloc 6))) ";" ((f,(intloc 4)) := (intloc 5))),(Stop SCM+FSA)))) by SCMFSA6A:35
.= 21 by A1 ;
set j1 = (intloc 2) := (intloc 1);
set j2 = SubFrom ((intloc 2),(intloc 0));
set j3 = (intloc 3) :=len f;
set body1 = ((((intloc 2) := (intloc 1)) ";" (SubFrom ((intloc 2),(intloc 0)))) ";" ((intloc 3) :=len f)) ";" (Times ((intloc 2),(((((((intloc 4) := (intloc 3)) ";" (SubFrom ((intloc 3),(intloc 0)))) ";" ((intloc 5) := (f,(intloc 3)))) ";" ((intloc 6) := (f,(intloc 4)))) ";" (SubFrom ((intloc 6),(intloc 5)))) ";" (if>0 ((intloc 6),((((intloc 6) := (f,(intloc 4))) ";" ((f,(intloc 3)) := (intloc 6))) ";" ((f,(intloc 4)) := (intloc 5))),(Stop SCM+FSA))))));
A3: card (((((intloc 2) := (intloc 1)) ";" (SubFrom ((intloc 2),(intloc 0)))) ";" ((intloc 3) :=len f)) ";" (Times ((intloc 2),(((((((intloc 4) := (intloc 3)) ";" (SubFrom ((intloc 3),(intloc 0)))) ";" ((intloc 5) := (f,(intloc 3)))) ";" ((intloc 6) := (f,(intloc 4)))) ";" (SubFrom ((intloc 6),(intloc 5)))) ";" (if>0 ((intloc 6),((((intloc 6) := (f,(intloc 4))) ";" ((f,(intloc 3)) := (intloc 6))) ";" ((f,(intloc 4)) := (intloc 5))),(Stop SCM+FSA))))))) = (card ((((intloc 2) := (intloc 1)) ";" (SubFrom ((intloc 2),(intloc 0)))) ";" ((intloc 3) :=len f))) + (card (Times ((intloc 2),(((((((intloc 4) := (intloc 3)) ";" (SubFrom ((intloc 3),(intloc 0)))) ";" ((intloc 5) := (f,(intloc 3)))) ";" ((intloc 6) := (f,(intloc 4)))) ";" (SubFrom ((intloc 6),(intloc 5)))) ";" (if>0 ((intloc 6),((((intloc 6) := (f,(intloc 4))) ";" ((f,(intloc 3)) := (intloc 6))) ";" ((f,(intloc 4)) := (intloc 5))),(Stop SCM+FSA))))))) by SCMFSA6A:21
.= 6 + (card (Times ((intloc 2),(((((((intloc 4) := (intloc 3)) ";" (SubFrom ((intloc 3),(intloc 0)))) ";" ((intloc 5) := (f,(intloc 3)))) ";" ((intloc 6) := (f,(intloc 4)))) ";" (SubFrom ((intloc 6),(intloc 5)))) ";" (if>0 ((intloc 6),((((intloc 6) := (f,(intloc 4))) ";" ((f,(intloc 3)) := (intloc 6))) ";" ((f,(intloc 4)) := (intloc 5))),(Stop SCM+FSA))))))) by Th15
.= 6 + (21 + 7) by A2, SCMFSA8C:94
.= 34 ;
set k2 = (intloc 2) := (intloc 0);
set k3 = (intloc 3) := (intloc 0);
set k4 = (intloc 4) := (intloc 0);
set k5 = (intloc 5) := (intloc 0);
set k6 = (intloc 6) := (intloc 0);
A4: card ((((((intloc 2) := (intloc 0)) ";" ((intloc 3) := (intloc 0))) ";" ((intloc 4) := (intloc 0))) ";" ((intloc 5) := (intloc 0))) ";" ((intloc 6) := (intloc 0))) = (card (((((intloc 2) := (intloc 0)) ";" ((intloc 3) := (intloc 0))) ";" ((intloc 4) := (intloc 0))) ";" ((intloc 5) := (intloc 0)))) + 2 by SCMFSA6A:34
.= ((card ((((intloc 2) := (intloc 0)) ";" ((intloc 3) := (intloc 0))) ";" ((intloc 4) := (intloc 0)))) + 2) + 2 by SCMFSA6A:34
.= (card ((((intloc 2) := (intloc 0)) ";" ((intloc 3) := (intloc 0))) ";" ((intloc 4) := (intloc 0)))) + 4
.= 6 + 4 by Th15
.= 10 ;
set k7 = (intloc 1) :=len f;
set Ct = card (Times ((intloc 1),(((((intloc 2) := (intloc 1)) ";" (SubFrom ((intloc 2),(intloc 0)))) ";" ((intloc 3) :=len f)) ";" (Times ((intloc 2),(((((((intloc 4) := (intloc 3)) ";" (SubFrom ((intloc 3),(intloc 0)))) ";" ((intloc 5) := (f,(intloc 3)))) ";" ((intloc 6) := (f,(intloc 4)))) ";" (SubFrom ((intloc 6),(intloc 5)))) ";" (if>0 ((intloc 6),((((intloc 6) := (f,(intloc 4))) ";" ((f,(intloc 3)) := (intloc 6))) ";" ((f,(intloc 4)) := (intloc 5))),(Stop SCM+FSA)))))))));
A5: card (Times ((intloc 1),(((((intloc 2) := (intloc 1)) ";" (SubFrom ((intloc 2),(intloc 0)))) ";" ((intloc 3) :=len f)) ";" (Times ((intloc 2),(((((((intloc 4) := (intloc 3)) ";" (SubFrom ((intloc 3),(intloc 0)))) ";" ((intloc 5) := (f,(intloc 3)))) ";" ((intloc 6) := (f,(intloc 4)))) ";" (SubFrom ((intloc 6),(intloc 5)))) ";" (if>0 ((intloc 6),((((intloc 6) := (f,(intloc 4))) ";" ((f,(intloc 3)) := (intloc 6))) ";" ((f,(intloc 4)) := (intloc 5))),(Stop SCM+FSA))))))))) = 34 + 7 by A3, SCMFSA8C:94;
thus card (bubble-sort f) = (card (((((((intloc 2) := (intloc 0)) ";" ((intloc 3) := (intloc 0))) ";" ((intloc 4) := (intloc 0))) ";" ((intloc 5) := (intloc 0))) ";" ((intloc 6) := (intloc 0))) ";" ((intloc 1) :=len f))) + (card (Times ((intloc 1),(((((intloc 2) := (intloc 1)) ";" (SubFrom ((intloc 2),(intloc 0)))) ";" ((intloc 3) :=len f)) ";" (Times ((intloc 2),(((((((intloc 4) := (intloc 3)) ";" (SubFrom ((intloc 3),(intloc 0)))) ";" ((intloc 5) := (f,(intloc 3)))) ";" ((intloc 6) := (f,(intloc 4)))) ";" (SubFrom ((intloc 6),(intloc 5)))) ";" (if>0 ((intloc 6),((((intloc 6) := (f,(intloc 4))) ";" ((f,(intloc 3)) := (intloc 6))) ";" ((f,(intloc 4)) := (intloc 5))),(Stop SCM+FSA)))))))))) by SCMFSA6A:21
.= (10 + 2) + (card (Times ((intloc 1),(((((intloc 2) := (intloc 1)) ";" (SubFrom ((intloc 2),(intloc 0)))) ";" ((intloc 3) :=len f)) ";" (Times ((intloc 2),(((((((intloc 4) := (intloc 3)) ";" (SubFrom ((intloc 3),(intloc 0)))) ";" ((intloc 5) := (f,(intloc 3)))) ";" ((intloc 6) := (f,(intloc 4)))) ";" (SubFrom ((intloc 6),(intloc 5)))) ";" (if>0 ((intloc 6),((((intloc 6) := (f,(intloc 4))) ";" ((f,(intloc 3)) := (intloc 6))) ";" ((f,(intloc 4)) := (intloc 5))),(Stop SCM+FSA)))))))))) by A4, SCMFSA6A:34
.= 53 by A5 ; :: thesis: verum