let a be Int_position; :: thesis: 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; :: thesis: 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; :: thesis: 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; :: thesis: 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; :: thesis: (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 ; :: thesis: verum

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; :: thesis: 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; :: thesis: 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; :: thesis: 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; :: thesis: (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 ; :: thesis: verum