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
for n being Nat holds IC (p +* (Start-At (n,S))) = n
let S be non empty with_non-empty_values IC-Ins-separated Mem-Struct over N; :: thesis: for p being PartState of S
for n being Nat holds IC (p +* (Start-At (n,S))) = n
let p be PartState of S; :: thesis: for n being Nat holds IC (p +* (Start-At (n,S))) = n
let n be Nat; :: thesis: IC (p +* (Start-At (n,S))) = n
A1: IC in dom (Start-At (n,S)) by Th15;
(Start-At (n,S)) . (IC ) = n by FUNCOP_1:72;
hence IC (p +* (Start-At (n,S))) = n by A1, FUNCT_4:13; :: thesis: verum