let s be State of SCMPDS ; :: thesis: for md, m3, n0 being Element of NAT st s . GBP = 0 & s . (intpos 5) > 0 & s . (intpos 4) = m3 + (s . (intpos 5)) & m3 = (s . (intpos 3)) - 1 & s . (intpos 2) = md & md >= n0 + 1 & md <= m3 & n0 >= 7 holds
( while>0 GBP ,5,(((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))) is_closed_on s & while>0 GBP ,5,(((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))) is_halting_on s )
let md, m3, n0 be Element of NAT ; :: thesis: ( s . GBP = 0 & s . (intpos 5) > 0 & s . (intpos 4) = m3 + (s . (intpos 5)) & m3 = (s . (intpos 3)) - 1 & s . (intpos 2) = md & md >= n0 + 1 & md <= m3 & n0 >= 7 implies ( while>0 GBP ,5,(((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))) is_closed_on s & while>0 GBP ,5,(((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))) is_halting_on s ) )
set a = GBP ;
assume A1:
( s . GBP = 0 & s . (intpos 5) > 0 & s . (intpos 4) = m3 + (s . (intpos 5)) & m3 = (s . (intpos 3)) - 1 & s . (intpos 2) = md & md >= n0 + 1 & md <= m3 & n0 >= 7 )
; :: thesis: ( while>0 GBP ,5,(((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))) is_closed_on s & while>0 GBP ,5,(((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))) is_halting_on s )
then
n0 + 1 >= 7 + 1
by XREAL_1:8;
then A2:
md >= 8
by A1, XXREAL_0:2;
A3:
DataLoc (s . GBP ),5 = intpos (0 + 5)
by A1, SCMP_GCD:5;
now let v be
State of
SCMPDS ;
:: thesis: ( v . (intpos 4) = ((v . (intpos 3)) - 1) + (v . (intpos 5)) & md <= (v . (intpos 3)) - 1 & v . (intpos 2) = s . (intpos 2) & v . GBP = s . GBP & v . (DataLoc (s . GBP ),5) > 0 implies ( (IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . GBP = v . GBP & ((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1)))) is_closed_on v & ((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1)))) is_halting_on v & (IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (DataLoc (s . GBP ),5) < v . (DataLoc (s . GBP ),5) & (IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 4) = (((IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 3)) - 1) + ((IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 5)) & md <= ((IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 3)) - 1 & (IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 2) = v . (intpos 2) ) )assume A4:
(
v . (intpos 4) = ((v . (intpos 3)) - 1) + (v . (intpos 5)) &
md <= (v . (intpos 3)) - 1 &
v . (intpos 2) = s . (intpos 2) &
v . GBP = s . GBP &
v . (DataLoc (s . GBP ),5) > 0 )
;
:: thesis: ( (IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . GBP = v . GBP & ((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1)))) is_closed_on v & ((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1)))) is_halting_on v & (IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (DataLoc (s . GBP ),5) < v . (DataLoc (s . GBP ),5) & (IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 4) = (((IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 3)) - 1) + ((IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 5)) & md <= ((IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 3)) - 1 & (IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 2) = v . (intpos 2) )then reconsider mm =
(v . (intpos 3)) - 1 as
Element of
NAT by INT_1:16;
A5:
(
v . (intpos 4) = mm + (v . (intpos 5)) &
md <= mm )
by A4;
set Iv =
IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),
v;
thus
(IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . GBP = v . GBP
by A1, A2, A3, A4, A5, Lm20;
:: thesis: ( ((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1)))) is_closed_on v & ((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1)))) is_halting_on v & (IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (DataLoc (s . GBP ),5) < v . (DataLoc (s . GBP ),5) & (IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 4) = (((IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 3)) - 1) + ((IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 5)) & md <= ((IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 3)) - 1 & (IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 2) = v . (intpos 2) )thus
(
((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1)))) is_closed_on v &
((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1)))) is_halting_on v )
by A1, A2, A3, A4, A5, Lm20;
:: thesis: ( (IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (DataLoc (s . GBP ),5) < v . (DataLoc (s . GBP ),5) & (IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 4) = (((IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 3)) - 1) + ((IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 5)) & md <= ((IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 3)) - 1 & (IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 2) = v . (intpos 2) )thus
(IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (DataLoc (s . GBP ),5) < v . (DataLoc (s . GBP ),5)
by A1, A2, A3, A4, A5, Lm20;
:: thesis: ( (IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 4) = (((IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 3)) - 1) + ((IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 5)) & md <= ((IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 3)) - 1 & (IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 2) = v . (intpos 2) )thus
(IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 4) = (((IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 3)) - 1) + ((IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 5))
by A1, A2, A3, A4, A5, Lm20;
:: thesis: ( md <= ((IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 3)) - 1 & (IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 2) = v . (intpos 2) )
(IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 3) >= v . (intpos 3)
by A1, A2, A3, A4, A5, Lm20;
then
((IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 3)) - 1
>= (v . (intpos 3)) - 1
by XREAL_1:11;
hence
md <= ((IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 3)) - 1
by A4, XXREAL_0:2;
:: thesis: (IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 2) = v . (intpos 2)thus
(IExec (((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))),v) . (intpos 2) = v . (intpos 2)
by A1, A2, A3, A4, A5, Lm20;
:: thesis: verum end;
hence
( while>0 GBP ,5,(((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))) is_closed_on s & while>0 GBP ,5,(((while>0 GBP ,5,(((((GBP ,7 := GBP ,5) ';' (AddTo GBP ,5,(- 1))) ';' (GBP ,6 := (intpos 4),0 )) ';' (SubFrom GBP ,6,(intpos 2),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,4,(- 1)) ';' (AddTo GBP ,7,(- 1))),(Load (GBP ,5 := 0 ))))) ';' (while>0 GBP ,7,(((((GBP ,5 := GBP ,7) ';' (AddTo GBP ,7,(- 1))) ';' (GBP ,6 := (intpos 2),0 )) ';' (SubFrom GBP ,6,(intpos 3),0 )) ';' (if>0 GBP ,6,((AddTo GBP ,3,1) ';' (AddTo GBP ,5,(- 1))),(Load (GBP ,7 := 0 )))))) ';' (if>0 GBP ,5,((((((GBP ,6 := (intpos 4),0 ) ';' ((intpos 4),0 := (intpos 3),0 )) ';' ((intpos 3),0 := GBP ,6)) ';' (AddTo GBP ,5,(- 2))) ';' (AddTo GBP ,3,1)) ';' (AddTo GBP ,4,(- 1))))) is_halting_on s )
by A1, Lm17, Th7; :: thesis: verum