let a be Int_position; for P being Instruction-Sequence of SCMPDS
for s being 0 -started State of SCMPDS
for i being No-StopCode parahalting Instruction of SCMPDS
for j being shiftable parahalting Instruction of SCMPDS holds (IExec ((i ';' j),P,s)) . a = (Exec (j,(Exec (i,s)))) . a
let P be Instruction-Sequence of SCMPDS; for s being 0 -started State of SCMPDS
for i being No-StopCode parahalting Instruction of SCMPDS
for j being shiftable parahalting Instruction of SCMPDS holds (IExec ((i ';' j),P,s)) . a = (Exec (j,(Exec (i,s)))) . a
let s be 0 -started State of SCMPDS; for i being No-StopCode parahalting Instruction of SCMPDS
for j being shiftable parahalting Instruction of SCMPDS holds (IExec ((i ';' j),P,s)) . a = (Exec (j,(Exec (i,s)))) . a
let i be No-StopCode parahalting Instruction of SCMPDS; for j being shiftable parahalting Instruction of SCMPDS holds (IExec ((i ';' j),P,s)) . a = (Exec (j,(Exec (i,s)))) . a
let j be shiftable parahalting Instruction of SCMPDS; (IExec ((i ';' j),P,s)) . a = (Exec (j,(Exec (i,s)))) . a
set Mi = Load i;
thus (IExec ((i ';' j),P,s)) . a =
(IExec (((Load i) ';' j),P,s)) . a
.=
(Exec (j,(IExec ((Load i),P,s)))) . a
by Th28
.=
(Exec (j,(Exec (i,s)))) . a
by Th27
; verum