let N be with_zero set ; :: thesis: for S being non empty with_non-empty_values IC-Ins-separated Mem-Struct over N
for s being State of S holds Start-At ((IC s),S) = s | {(IC )}
let S be non empty with_non-empty_values IC-Ins-separated Mem-Struct over N; :: thesis: for s being State of S holds Start-At ((IC s),S) = s | {(IC )}
let s be State of S; :: thesis: Start-At ((IC s),S) = s | {(IC )}
A1: IC in dom s by Th2;
thus Start-At ((IC s),S) = {[(IC ),(s . (IC ))]} by FUNCT_4:82
.= s | {(IC )} by A1, GRFUNC_1:28 ; :: thesis: verum