set a = GBP ;
let s be State of SCMPDS ; for m4, md being Element of NAT st s . GBP = 0 & s . (intpos 4) = m4 + (s . (intpos 5)) & m4 >= 8 & s . (intpos 2) = md & md >= 8 holds
( 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 )))) is_closed_on s & 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 )))) is_halting_on s )
let m4, md be Element of NAT ; ( s . GBP = 0 & s . (intpos 4) = m4 + (s . (intpos 5)) & m4 >= 8 & s . (intpos 2) = md & md >= 8 implies ( 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 )))) is_closed_on s & 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 )))) is_halting_on s ) )
assume that
A1:
s . GBP = 0
and
A2:
s . (intpos 4) = m4 + (s . (intpos 5))
and
A3:
m4 >= 8
and
A4:
s . (intpos 2) = md
and
A5:
md >= 8
; ( 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 )))) is_closed_on s & 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 )))) is_halting_on s )
set b = DataLoc (s . GBP ),5;
A6:
DataLoc (s . GBP ),5 = intpos (0 + 5)
by A1, SCMP_GCD:5;
now let v be
State of
SCMPDS ;
( v . (intpos 4) >= m4 + (v . (DataLoc (s . GBP ),5)) & v . (intpos 2) = s . (intpos 2) & v . GBP = s . GBP & v . (DataLoc (s . GBP ),5) > 0 implies ( (IExec (((((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 )))),v) . GBP = v . GBP & ((((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 ))) is_closed_on v & ((((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 ))) is_halting_on v & (IExec (((((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 )))),v) . (DataLoc (s . GBP ),5) < v . (DataLoc (s . GBP ),5) & (IExec (((((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 )))),v) . (intpos 4) >= m4 + ((IExec (((((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 )))),v) . (DataLoc (s . GBP ),5)) & (IExec (((((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 )))),v) . (intpos 2) = v . (intpos 2) ) )assume that A7:
v . (intpos 4) >= m4 + (v . (DataLoc (s . GBP ),5))
and A8:
v . (intpos 2) = s . (intpos 2)
and A9:
v . GBP = s . GBP
and A10:
v . (DataLoc (s . GBP ),5) > 0
;
( (IExec (((((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 )))),v) . GBP = v . GBP & ((((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 ))) is_closed_on v & ((((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 ))) is_halting_on v & (IExec (((((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 )))),v) . (DataLoc (s . GBP ),5) < v . (DataLoc (s . GBP ),5) & (IExec (((((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 )))),v) . (intpos 4) >= m4 + ((IExec (((((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 )))),v) . (DataLoc (s . GBP ),5)) & (IExec (((((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 )))),v) . (intpos 2) = v . (intpos 2) )A11:
m4 + (v . (DataLoc (s . GBP ),5)) > m4 + 0
by A10, XREAL_1:8;
then reconsider ME =
v . (intpos 4) as
Element of
NAT by A7, INT_1:16;
v . (intpos 4) >= m4
by A7, A11, XXREAL_0:2;
then A12:
ME >= 8
by A3, XXREAL_0:2;
then A13:
(
v . (intpos md) < v . (intpos ME) implies (
(IExec (((((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 )))),v) . (intpos 5) = (v . (intpos 5)) - 1 &
(IExec (((((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 )))),v) . (intpos 4) = (v . (intpos 4)) - 1 &
(IExec (((((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 )))),v) . (intpos 7) = (v . (intpos 5)) - 1 ) )
by A1, A4, A5, A8, A9, Lm8;
thus
(IExec (((((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 )))),v) . GBP = v . GBP
by A1, A4, A5, A8, A9, A12, Lm8;
( ((((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 ))) is_closed_on v & ((((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 ))) is_halting_on v & (IExec (((((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 )))),v) . (DataLoc (s . GBP ),5) < v . (DataLoc (s . GBP ),5) & (IExec (((((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 )))),v) . (intpos 4) >= m4 + ((IExec (((((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 )))),v) . (DataLoc (s . GBP ),5)) & (IExec (((((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 )))),v) . (intpos 2) = v . (intpos 2) )thus
(
((((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 ))) is_closed_on v &
((((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 ))) is_halting_on v )
by SCMPDS_6:34, SCMPDS_6:35;
( (IExec (((((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 )))),v) . (DataLoc (s . GBP ),5) < v . (DataLoc (s . GBP ),5) & (IExec (((((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 )))),v) . (intpos 4) >= m4 + ((IExec (((((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 )))),v) . (DataLoc (s . GBP ),5)) & (IExec (((((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 )))),v) . (intpos 2) = v . (intpos 2) )A14:
(
v . (intpos md) >= v . (intpos ME) implies (
(IExec (((((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 )))),v) . (intpos 5) = 0 &
(IExec (((((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 )))),v) . (intpos 4) = v . (intpos 4) &
(IExec (((((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 )))),v) . (intpos 7) = v . (intpos 5) ) )
by A1, A4, A5, A8, A9, A12, Lm8;
hereby (IExec (((((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 )))),v) . (intpos 2) = v . (intpos 2)
per cases
( v . (intpos md) < v . (intpos ME) or v . (intpos md) >= v . (intpos ME) )
;
suppose A15:
v . (intpos md) < v . (intpos ME)
;
( (IExec (((((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 )))),v) . (DataLoc (s . GBP ),5) < v . (DataLoc (s . GBP ),5) & (IExec (((((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 )))),v) . (intpos 4) >= m4 + ((IExec (((((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 )))),v) . (DataLoc (s . GBP ),5)) )hence
(IExec (((((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 )))),v) . (DataLoc (s . GBP ),5) < v . (DataLoc (s . GBP ),5)
by A6, A13, XREAL_1:148;
(IExec (((((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 )))),v) . (intpos 4) >= m4 + ((IExec (((((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 )))),v) . (DataLoc (s . GBP ),5))
(m4 + (v . (DataLoc (s . GBP ),5))) - 1
= m4 + ((IExec (((((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 )))),v) . (DataLoc (s . GBP ),5))
by A6, A13, A15;
hence
(IExec (((((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 )))),v) . (intpos 4) >= m4 + ((IExec (((((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 )))),v) . (DataLoc (s . GBP ),5))
by A7, A13, A15, XREAL_1:11;
verum end; suppose A16:
v . (intpos md) >= v . (intpos ME)
;
( (IExec (((((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 )))),v) . (DataLoc (s . GBP ),5) < v . (DataLoc (s . GBP ),5) & (IExec (((((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 )))),v) . (intpos 4) >= m4 + ((IExec (((((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 )))),v) . (DataLoc (s . GBP ),5)) )hence
(IExec (((((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 )))),v) . (DataLoc (s . GBP ),5) < v . (DataLoc (s . GBP ),5)
by A1, A4, A5, A6, A8, A9, A10, A12, Lm8;
(IExec (((((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 )))),v) . (intpos 4) >= m4 + ((IExec (((((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 )))),v) . (DataLoc (s . GBP ),5))
m4 + ((IExec (((((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 )))),v) . (DataLoc (s . GBP ),5)) < m4 + (v . (DataLoc (s . GBP ),5))
by A6, A10, A14, A16, XREAL_1:8;
hence
(IExec (((((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 )))),v) . (intpos 4) >= m4 + ((IExec (((((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 )))),v) . (DataLoc (s . GBP ),5))
by A7, A14, A16, XXREAL_0:2;
verum end; thus
(IExec (((((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 )))),v) . (intpos 2) = v . (intpos 2)
by A1, A4, A5, A8, A9, A12, Lm8;
verum end;
hence
( 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 )))) is_closed_on s & 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 )))) is_halting_on s )
by A2, A6, Lm7, Th5; verum