let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty stored-program IC-Ins-separated definite realistic COM-Struct of N
for k being Element of NAT
for p being PartState of S st IC S in dom p holds
IncrIC (NPP p),k = (DataPart p) +* (Start-At ((IC p) + k),S)
let S be non empty stored-program IC-Ins-separated definite realistic COM-Struct of N; :: thesis: for k being Element of NAT
for p being PartState of S st IC S in dom p holds
IncrIC (NPP p),k = (DataPart p) +* (Start-At ((IC p) + k),S)
let k be Element of NAT ; :: thesis: for p being PartState of S st IC S in dom p holds
IncrIC (NPP p),k = (DataPart p) +* (Start-At ((IC p) + k),S)
let p be PartState of S; :: thesis: ( IC S in dom p implies IncrIC (NPP p),k = (DataPart p) +* (Start-At ((IC p) + k),S) )
A: dom (Start-At ((IC p) + k),S) = {(IC S)} by FUNCOP_1:19
.= dom (Start-At (IC p),S) by FUNCOP_1:19 ;
assume Z: IC S in dom p ; :: thesis: IncrIC (NPP p),k = (DataPart p) +* (Start-At ((IC p) + k),S)
hence IncrIC (NPP p),k = (NPP p) +* (Start-At ((IC p) + k),S) by Th47
.= ((DataPart p) +* (Start-At (IC p),S)) +* (Start-At ((IC p) + k),S) by Z, Th49
.= (DataPart p) +* (Start-At ((IC p) + k),S) by A, FUNCT_4:78 ;
:: thesis: verum