let k be Nat; :: thesis: for N being with_zero set
for S being non empty with_non-empty_values IC-Ins-separated Mem-Struct over N
for p being PartState of S holds IC in dom (p +* (Start-At (k,S)))
let N be with_zero set ; :: thesis: for S being non empty with_non-empty_values IC-Ins-separated Mem-Struct over N
for p being PartState of S holds IC in dom (p +* (Start-At (k,S)))
let S be non empty with_non-empty_values IC-Ins-separated Mem-Struct over 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)))
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