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 (IncrIC (p,k)) . (IC S) = (IC 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 (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
IC S in dom (Start-At (((IC p) + k),S)) by Th52;
hence (IncrIC (p,k)) . (IC S) = (Start-At (((IC p) + k),S)) . (IC S) by FUNCT_4:14
.= IC (Start-At (((IC p) + k),S))
.= (IC p) + k by FUNCOP_1:87 ;
:: thesis: verum