let s be State of SCM+FSA; :: thesis: for p being Instruction-Sequence of SCM+FSA

for a being Int-Location

for J being good MacroInstruction of SCM+FSA st ( s . (intloc 0) = 1 or a is read-write ) holds

((StepTimes (a,J,p,s)) . 0) . (1 -stRWNotIn ({a} \/ (UsedILoc J))) = s . a

let p be Instruction-Sequence of SCM+FSA; :: thesis: for a being Int-Location

for J being good MacroInstruction of SCM+FSA st ( s . (intloc 0) = 1 or a is read-write ) holds

((StepTimes (a,J,p,s)) . 0) . (1 -stRWNotIn ({a} \/ (UsedILoc J))) = s . a

let a be Int-Location; :: thesis: for J being good MacroInstruction of SCM+FSA st ( s . (intloc 0) = 1 or a is read-write ) holds

((StepTimes (a,J,p,s)) . 0) . (1 -stRWNotIn ({a} \/ (UsedILoc J))) = s . a

let J be good MacroInstruction of SCM+FSA ; :: thesis: ( ( s . (intloc 0) = 1 or a is read-write ) implies ((StepTimes (a,J,p,s)) . 0) . (1 -stRWNotIn ({a} \/ (UsedILoc J))) = s . a )

set I = J;

set ST = StepTimes (a,J,p,s);

set au = 1 -stRWNotIn ({a} \/ (UsedILoc J));

set Is = Initialized s;

assume A1: ( s . (intloc 0) = 1 or a is read-write ) ; :: thesis: ((StepTimes (a,J,p,s)) . 0) . (1 -stRWNotIn ({a} \/ (UsedILoc J))) = s . a

A2: ( a = intloc 0 or a is read-write ) by SCMFSA_M:def 2;

thus ((StepTimes (a,J,p,s)) . 0) . (1 -stRWNotIn ({a} \/ (UsedILoc J))) = (Exec (((1 -stRWNotIn ({a} \/ (UsedILoc J))) := a),(Initialized s))) . (1 -stRWNotIn ({a} \/ (UsedILoc J))) by SCMFSA_9:def 5

.= (Initialized s) . a by SCMFSA_2:63

.= s . a by A1, A2, SCMFSA_M:9, SCMFSA_M:37 ; :: thesis: verum

for a being Int-Location

for J being good MacroInstruction of SCM+FSA st ( s . (intloc 0) = 1 or a is read-write ) holds

((StepTimes (a,J,p,s)) . 0) . (1 -stRWNotIn ({a} \/ (UsedILoc J))) = s . a

let p be Instruction-Sequence of SCM+FSA; :: thesis: for a being Int-Location

for J being good MacroInstruction of SCM+FSA st ( s . (intloc 0) = 1 or a is read-write ) holds

((StepTimes (a,J,p,s)) . 0) . (1 -stRWNotIn ({a} \/ (UsedILoc J))) = s . a

let a be Int-Location; :: thesis: for J being good MacroInstruction of SCM+FSA st ( s . (intloc 0) = 1 or a is read-write ) holds

((StepTimes (a,J,p,s)) . 0) . (1 -stRWNotIn ({a} \/ (UsedILoc J))) = s . a

let J be good MacroInstruction of SCM+FSA ; :: thesis: ( ( s . (intloc 0) = 1 or a is read-write ) implies ((StepTimes (a,J,p,s)) . 0) . (1 -stRWNotIn ({a} \/ (UsedILoc J))) = s . a )

set I = J;

set ST = StepTimes (a,J,p,s);

set au = 1 -stRWNotIn ({a} \/ (UsedILoc J));

set Is = Initialized s;

assume A1: ( s . (intloc 0) = 1 or a is read-write ) ; :: thesis: ((StepTimes (a,J,p,s)) . 0) . (1 -stRWNotIn ({a} \/ (UsedILoc J))) = s . a

A2: ( a = intloc 0 or a is read-write ) by SCMFSA_M:def 2;

thus ((StepTimes (a,J,p,s)) . 0) . (1 -stRWNotIn ({a} \/ (UsedILoc J))) = (Exec (((1 -stRWNotIn ({a} \/ (UsedILoc J))) := a),(Initialized s))) . (1 -stRWNotIn ({a} \/ (UsedILoc J))) by SCMFSA_9:def 5

.= (Initialized s) . a by SCMFSA_2:63

.= s . a by A1, A2, SCMFSA_M:9, SCMFSA_M:37 ; :: thesis: verum