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 k, l being Nat holds (p +* (Start-At (k,S))) +* (Start-At (l,S)) = p +* (Start-At (l,S))
let S be non empty with_non-empty_values IC-Ins-separated Mem-Struct over N; :: thesis: for p being PartState of S
for k, l being Nat holds (p +* (Start-At (k,S))) +* (Start-At (l,S)) = p +* (Start-At (l,S))
let p be PartState of S; :: thesis: for k, l being Nat holds (p +* (Start-At (k,S))) +* (Start-At (l,S)) = p +* (Start-At (l,S))
let k, l be Nat; :: thesis: (p +* (Start-At (k,S))) +* (Start-At (l,S)) = p +* (Start-At (l,S))
dom (Start-At (k,S)) = {(IC )}
.= dom (Start-At (l,S)) ;
hence (p +* (Start-At (k,S))) +* (Start-At (l,S)) = p +* (Start-At (l,S)) by FUNCT_4:74; :: thesis: verum