let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty stored-program IC-Ins-separated definite realistic COM-Struct of N
for p being PartState of S st Start-At (0,S) c= p holds
IC p = 0
let S be non empty stored-program IC-Ins-separated definite realistic COM-Struct of N; :: thesis: for p being PartState of S st Start-At (0,S) c= p holds
IC p = 0
let p be PartState of S; :: thesis: ( Start-At (0,S) c= p implies IC p = 0 )
A1: IC (Start-At (0,S)) = 0 by Def16;
A2: IC in dom (Start-At (0,S)) by Def16;
assume Start-At (0,S) c= p ; :: thesis: IC p = 0
hence IC p = 0 by A1, A2, GRFUNC_1:8; :: thesis: verum