let k be Nat; :: thesis: for N being 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 st IC in dom p holds
IncIC (p,k) = (DataPart p) +* (Start-At (((IC p) + k),S))
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 IC in dom p holds
IncIC (p,k) = (DataPart p) +* (Start-At (((IC p) + k),S))
let S be non empty with_non-empty_values IC-Ins-separated Mem-Struct over N; :: thesis: for p being PartState of S st IC in dom p holds
IncIC (p,k) = (DataPart p) +* (Start-At (((IC p) + k),S))
let p be PartState of S; :: thesis: ( IC in dom p implies IncIC (p,k) = (DataPart p) +* (Start-At (((IC p) + k),S)) )
A1: dom (Start-At (((IC p) + k),S)) = {(IC )}
.= dom (Start-At ((IC p),S)) ;
assume A2: IC in dom p ; :: thesis: IncIC (p,k) = (DataPart p) +* (Start-At (((IC p) + k),S))
thus IncIC (p,k) = ((DataPart p) +* (Start-At ((IC p),S))) +* (Start-At (((IC p) + k),S)) by A2, Th26
.= (DataPart p) +* (Start-At (((IC p) + k),S)) by A1, FUNCT_4:74 ; :: thesis: verum