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
for d being data-only PartState of S holds IC (p +* d) = IC p
let S be non empty with_non-empty_values IC-Ins-separated Mem-Struct over N; :: thesis: for p being PartState of S
for d being data-only PartState of S holds IC (p +* d) = IC p
let p be PartState of S; :: thesis: for d being data-only PartState of S holds IC (p +* d) = IC p
let d be data-only PartState of S; :: thesis: IC (p +* d) = IC p
A1: not IC in dom d by Th10;
thus IC (p +* d) = IC p by A1, FUNCT_4:11; :: thesis: verum