let p be Instruction-Sequence of SCM+FSA; :: thesis: for s being State of SCM+FSA
for a being read-write Int-Location
for I being MacroInstruction of SCM+FSA
for k being Nat st ((StepWhile>0 (a,I,p,s)) . k) . a <= 0 holds
DataPart ((StepWhile>0 (a,I,p,s)) . (k + 1)) = DataPart ((StepWhile>0 (a,I,p,s)) . k)
let s be State of SCM+FSA; :: thesis: for a being read-write Int-Location
for I being MacroInstruction of SCM+FSA
for k being Nat st ((StepWhile>0 (a,I,p,s)) . k) . a <= 0 holds
DataPart ((StepWhile>0 (a,I,p,s)) . (k + 1)) = DataPart ((StepWhile>0 (a,I,p,s)) . k)
let a be read-write Int-Location; :: thesis: for I being MacroInstruction of SCM+FSA
for k being Nat st ((StepWhile>0 (a,I,p,s)) . k) . a <= 0 holds
DataPart ((StepWhile>0 (a,I,p,s)) . (k + 1)) = DataPart ((StepWhile>0 (a,I,p,s)) . k)
let I be MacroInstruction of SCM+FSA ; :: thesis: for k being Nat st ((StepWhile>0 (a,I,p,s)) . k) . a <= 0 holds
DataPart ((StepWhile>0 (a,I,p,s)) . (k + 1)) = DataPart ((StepWhile>0 (a,I,p,s)) . k)
let k be Nat; :: thesis: ( ((StepWhile>0 (a,I,p,s)) . k) . a <= 0 implies DataPart ((StepWhile>0 (a,I,p,s)) . (k + 1)) = DataPart ((StepWhile>0 (a,I,p,s)) . k) )
assume A1: ((StepWhile>0 (a,I,p,s)) . k) . a <= 0 ; :: thesis: DataPart ((StepWhile>0 (a,I,p,s)) . (k + 1)) = DataPart ((StepWhile>0 (a,I,p,s)) . k)
set SW = StepWhile>0 (a,I,p,s);
set PW = p +* (while>0 (a,I));
A2: while>0 (a,I) c= p +* (while>0 (a,I)) by FUNCT_4:25;
A3: DataPart (Initialize ((StepWhile>0 (a,I,p,s)) . k)) = DataPart ((StepWhile>0 (a,I,p,s)) . k) by MEMSTR_0:79;
then A4: ((StepWhile>0 (a,I,p,s)) . k) . a = (Initialize ((StepWhile>0 (a,I,p,s)) . k)) . a by SCMFSA_M:2;
thus DataPart ((StepWhile>0 (a,I,p,s)) . (k + 1)) = DataPart (Comput (((p +* (while>0 (a,I))) +* (while>0 (a,I))),(Initialize ((StepWhile>0 (a,I,p,s)) . k)),((LifeSpan (((p +* (while>0 (a,I))) +* I),(Initialize ((StepWhile>0 (a,I,p,s)) . k)))) + 2))) by SCMFSA_9:def 5
.= DataPart ((StepWhile>0 (a,I,p,s)) . k) by A1, A3, A4, Th29, A2 ; :: thesis: verum