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 p being FinPartState of S
for k being Element of NAT holds IC S in dom (IncrIC (p,k))
let S be non empty stored-program IC-Ins-separated definite realistic COM-Struct of N; :: thesis: for p being FinPartState of S
for k being Element of NAT holds IC S in dom (IncrIC (p,k))
let p be FinPartState of S; :: thesis: for k being Element of NAT holds IC S in dom (IncrIC (p,k))
let k be Element of NAT ; :: thesis: IC S in dom (IncrIC (p,k))
A1: dom (IncrIC (p,k)) = (dom p) \/ (dom (Start-At (((IC p) + k),S))) by FUNCT_4:def 1;
IC S in dom (Start-At (((IC p) + k),S)) by Th52;
hence IC S in dom (IncrIC (p,k)) by A1, XBOOLE_0:def 3; :: thesis: verum