set Ba = Bubble-Sort-Algorithm ;
set Ib = ((intloc 0) .--> 1) +* (Start-At (0,SCM+FSA));
let i be Element of NAT ; :: thesis: for s being State of SCM+FSA
for P being Instruction-Sequence of SCM+FSA st Bubble-Sort-Algorithm c= P holds
for w being FinSequence of INT st Initialized ((fsloc 0) .--> w) c= s holds
IC (Comput (P,s,i)) in dom Bubble-Sort-Algorithm
let s be State of SCM+FSA; :: thesis: for P being Instruction-Sequence of SCM+FSA st Bubble-Sort-Algorithm c= P holds
for w being FinSequence of INT st Initialized ((fsloc 0) .--> w) c= s holds
IC (Comput (P,s,i)) in dom Bubble-Sort-Algorithm
let P be Instruction-Sequence of SCM+FSA; :: thesis: ( Bubble-Sort-Algorithm c= P implies for w being FinSequence of INT st Initialized ((fsloc 0) .--> w) c= s holds
IC (Comput (P,s,i)) in dom Bubble-Sort-Algorithm )
assume A1: Bubble-Sort-Algorithm c= P ; :: thesis: for w being FinSequence of INT st Initialized ((fsloc 0) .--> w) c= s holds
IC (Comput (P,s,i)) in dom Bubble-Sort-Algorithm
let w be FinSequence of INT ; :: thesis: ( Initialized ((fsloc 0) .--> w) c= s implies IC (Comput (P,s,i)) in dom Bubble-Sort-Algorithm )
set x = (fsloc 0) .--> w;
assume A2: Initialized ((fsloc 0) .--> w) c= s ; :: thesis: IC (Comput (P,s,i)) in dom Bubble-Sort-Algorithm
set BSA = Bubble-Sort-Algorithm ;
Initialized ((fsloc 0) .--> w) = ((fsloc 0) .--> w) +* (Initialize ((intloc 0) .--> 1)) by SCMFSA6A:def 3;
then Initialize ((intloc 0) .--> 1) c= Initialized ((fsloc 0) .--> w) by FUNCT_4:25;
then Initialize ((intloc 0) .--> 1) c= s by A2, XBOOLE_1:1;
hence IC (Comput (P,s,i)) in dom Bubble-Sort-Algorithm by Lm26, A1, SCM_HALT:def 1; :: thesis: verum