let k be Nat; :: thesis: for N being with_non-empty_elements set
for S being non empty IC-Ins-separated Mem-Struct of N
for p being PartState of S holds IC in dom (p +* (Start-At (k,S)))
let N be with_non-empty_elements set ; :: thesis: for S being non empty IC-Ins-separated Mem-Struct of N
for p being PartState of S holds IC in dom (p +* (Start-At (k,S)))
let S be non empty IC-Ins-separated Mem-Struct of N; :: thesis: for p being PartState of S holds IC in dom (p +* (Start-At (k,S)))
let p be PartState of S; :: thesis: IC in dom (p +* (Start-At (k,S)))
dom (Start-At (k,S)) = {(IC )} by FUNCOP_1:13;
then IC in dom (Start-At (k,S)) by TARSKI:def 1;
hence IC in dom (p +* (Start-At (k,S))) by FUNCT_4:12; :: thesis: verum