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 (IncrIC p,k) = (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 IC (IncrIC p,k) = (IC p) + k
let p be FinPartState of S; :: thesis: for k being Element of NAT holds IC (IncrIC p,k) = (IC p) + k
let k be Element of NAT ; :: thesis: IC (IncrIC p,k) = (IC p) + k
dom (Start-At ((IC p) + k),S) = {(IC S)} by FUNCOP_1:19;
then A1: IC S in dom (Start-At ((IC p) + k),S) by TARSKI:def 1;
thus IC (IncrIC p,k) = (IncrIC p,k) . (IC S)
.= (Start-At ((IC p) + k),S) . (IC S) by A1, FUNCT_4:14
.= (IC p) + k by FUNCOP_1:87 ; :: thesis: verum