let N be with_non-empty_elements set ; :: thesis: for S being non empty IC-Ins-separated Mem-Struct of 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 IC-Ins-separated Mem-Struct of 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 Th57;
thus IC (p +* d) = IC p by A1, FUNCT_4:11; :: thesis: verum