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 s being State of S
for p being PartState of S st p +* (Start-At (k,S)) c= s holds
IC s = k
let N be with_zero set ; :: thesis: for S being non empty with_non-empty_values IC-Ins-separated Mem-Struct over N
for s being State of S
for p being PartState of S st p +* (Start-At (k,S)) c= s holds
IC s = k
let S be non empty with_non-empty_values IC-Ins-separated Mem-Struct over N; :: thesis: for s being State of S
for p being PartState of S st p +* (Start-At (k,S)) c= s holds
IC s = k
let s be State of S; :: thesis: for p being PartState of S st p +* (Start-At (k,S)) c= s holds
IC s = k
let p be PartState of S; :: thesis: ( p +* (Start-At (k,S)) c= s implies IC s = k )
assume A1: p +* (Start-At (k,S)) c= s ; :: thesis: IC s = k
IC in dom (p +* (Start-At (k,S))) by Th27;
hence IC s = IC (p +* (Start-At (k,S))) by A1, GRFUNC_1:2
.= k by Th16 ;
:: thesis: verum