let N be non empty with_non-empty_elements set ; :: thesis: for n being Element of NAT
for S being non empty stored-program IC-Ins-separated definite realistic COM-Struct of N
for s being State of S
for I being Program of S st I +* (Start-At (n,S)) c= s holds
IC s = n
let n be Element of NAT ; :: thesis: for S being non empty stored-program IC-Ins-separated definite realistic COM-Struct of N
for s being State of S
for I being Program of S st I +* (Start-At (n,S)) c= s holds
IC s = n
let S be non empty stored-program IC-Ins-separated definite realistic COM-Struct of N; :: thesis: for s being State of S
for I being Program of S st I +* (Start-At (n,S)) c= s holds
IC s = n
let s be State of S; :: thesis: for I being Program of S st I +* (Start-At (n,S)) c= s holds
IC s = n
let I be Program of S; :: thesis: ( I +* (Start-At (n,S)) c= s implies IC s = n )
assume A1: I +* (Start-At (n,S)) c= s ; :: thesis: IC s = n
IC S in dom (I +* (Start-At (n,S))) by Th65;
hence IC s = IC (I +* (Start-At (n,S))) by A1, GRFUNC_1:8
.= n by Th66 ;
:: thesis: verum