let N be with_zero set ; 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; 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; 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; (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; verum