let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty stored-program halting IC-Ins-separated definite realistic AMI-Struct of NAT ,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 halting IC-Ins-separated definite realistic AMI-Struct of NAT ,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)
X: dom (IncrIC p,k) = (dom p) \/ (dom (Start-At ((IC p) + k))) by FUNCT_4:def 1;
IC S in dom (Start-At ((IC p) + k)) by Th17;
hence IC S in dom (IncrIC p,k) by X, XBOOLE_0:def 3; :: thesis: verum