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 k being Nat holds (IC (IncIC (s,k))) -' k = IC s
let S be non empty with_non-empty_values IC-Ins-separated Mem-Struct over N; :: thesis: for s being State of S
for k being Nat holds (IC (IncIC (s,k))) -' k = IC s
let s be State of S; :: thesis: for k being Nat holds (IC (IncIC (s,k))) -' k = IC s
let k be Nat; :: thesis: (IC (IncIC (s,k))) -' k = IC s
thus (IC (IncIC (s,k))) -' k = ((IC s) + k) -' k by Th53
.= IC s by NAT_D:34 ; :: thesis: verum