let N be with_zero set ; :: thesis: for S being non empty with_non-empty_values IC-Ins-separated Mem-Struct over N
for p being PartState of S st Start-At (0,S) c= p holds
IC p = 0
let S be non empty with_non-empty_values IC-Ins-separated Mem-Struct over 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 Def11;
IC in dom (Start-At (0,S)) by Def11;
hence ( Start-At (0,S) c= p implies IC p = 0 ) by A1, GRFUNC_1:2; :: thesis: verum