let N be with_non-empty_elements set ; :: thesis: for S being non empty IC-Ins-separated Mem-Struct of N
for s being State of S
for k being Nat holds (IC (IncIC (s,k))) -' k = IC s
let S be non empty IC-Ins-separated Mem-Struct of 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 Th54
.= IC s by NAT_D:34 ; :: thesis: verum