let N be non empty with_non-empty_elements set ; :: thesis: for n being Element of NAT
for S being non empty stored-program IC-Ins-separated definite realistic COM-Struct of N
for p being PartState of S holds IC S in dom (p +* (Start-At (n,S)))
let n be Element of NAT ; :: thesis: for S being non empty stored-program IC-Ins-separated definite realistic COM-Struct of N
for p being PartState of S holds IC S in dom (p +* (Start-At (n,S)))
let S be non empty stored-program IC-Ins-separated definite realistic COM-Struct of N; :: thesis: for p being PartState of S holds IC S in dom (p +* (Start-At (n,S)))
let p be PartState of S; :: thesis: IC S in dom (p +* (Start-At (n,S)))
dom (Start-At (n,S)) = {(IC S)} by FUNCOP_1:19;
then IC S in dom (Start-At (n,S)) by TARSKI:def 1;
hence IC S in dom (p +* (Start-At (n,S))) by FUNCT_4:13; :: thesis: verum