let i be Element of NAT ; :: thesis: for s being State of SCM+FSA
for w being FinSequence of INT
for P being the Instructions of SCM+FSA -valued ManySortedSet of NAT st (Initialized Insert-Sort-Algorithm) +* ((fsloc 0) .--> w) c= s & Insert-Sort-Algorithm c= P holds
IC (Comput (P,s,i)) in dom Insert-Sort-Algorithm
let s be State of SCM+FSA; :: thesis: for w being FinSequence of INT
for P being the Instructions of SCM+FSA -valued ManySortedSet of NAT st (Initialized Insert-Sort-Algorithm) +* ((fsloc 0) .--> w) c= s & Insert-Sort-Algorithm c= P holds
IC (Comput (P,s,i)) in dom Insert-Sort-Algorithm
let w be FinSequence of INT ; :: thesis: for P being the Instructions of SCM+FSA -valued ManySortedSet of NAT st (Initialized Insert-Sort-Algorithm) +* ((fsloc 0) .--> w) c= s & Insert-Sort-Algorithm c= P holds
IC (Comput (P,s,i)) in dom Insert-Sort-Algorithm
let P be the Instructions of SCM+FSA -valued ManySortedSet of NAT ; :: thesis: ( (Initialized Insert-Sort-Algorithm) +* ((fsloc 0) .--> w) c= s & Insert-Sort-Algorithm c= P implies IC (Comput (P,s,i)) in dom Insert-Sort-Algorithm )
set IS = Insert-Sort-Algorithm ;
set Ii = Initialized Insert-Sort-Algorithm;
set x = (fsloc 0) .--> w;
dom (Initialized Insert-Sort-Algorithm) misses dom ((fsloc 0) .--> w) by SCMBSORT:46;
then A1: Initialized Insert-Sort-Algorithm c= (Initialized Insert-Sort-Algorithm) +* ((fsloc 0) .--> w) by FUNCT_4:33;
assume (Initialized Insert-Sort-Algorithm) +* ((fsloc 0) .--> w) c= s ; :: thesis: ( not Insert-Sort-Algorithm c= P or IC (Comput (P,s,i)) in dom Insert-Sort-Algorithm )
then A2: Initialized Insert-Sort-Algorithm c= s by A1, XBOOLE_1:1;
assume A3: Insert-Sort-Algorithm c= P ; :: thesis: IC (Comput (P,s,i)) in dom Insert-Sort-Algorithm
Insert-Sort-Algorithm is InitClosed by Lm12;
hence IC (Comput (P,s,i)) in dom Insert-Sort-Algorithm by SCM_HALT:def 1, A3, A2; :: thesis: verum