let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty IC-Ins-separated COM-Struct of N
for s being State of S holds Start-At (IC s),S = s | {(IC S)}
let S be non empty IC-Ins-separated COM-Struct of N; :: thesis: for s being State of S holds Start-At (IC s),S = s | {(IC S)}
let s be State of S; :: thesis: Start-At (IC s),S = s | {(IC S)}
A1: IC S in dom s by Th94;
thus Start-At (IC s),S = {[(IC S),(s . (IC S))]} by FUNCT_4:87
.= s | {(IC S)} by A1, GRFUNC_1:89 ; :: thesis: verum