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 (IncrIC p,k) . (IC S) = (IC 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 (IncrIC p,k) . (IC S) = (IC p) + k
let p be FinPartState of S; :: thesis: for k being Element of NAT holds (IncrIC p,k) . (IC S) = (IC p) + k
let k be Element of NAT ; :: thesis: (IncrIC p,k) . (IC S) = (IC p) + k
X: IC S in dom (Start-At ((IC p) + k)) by Th17;
hence (IncrIC p,k) . (IC S) = (Start-At ((IC p) + k)) . (IC S) by FUNCT_4:14
.= IC (Start-At ((IC p) + k)) by X, AMI_1:def 43
.= (IC p) + k by Th19 ;
:: thesis: verum