let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty stored-program IC-Ins-separated definite realistic COM-Struct of N
for p being PartState of S
for k being Nat holds IC (DecIC (p,k)) = (IC p) -' k
let S be non empty stored-program IC-Ins-separated definite realistic COM-Struct of N; :: thesis: for p being PartState of S
for k being Nat holds IC (DecIC (p,k)) = (IC p) -' k
let p be PartState of S; :: thesis: for k being Nat holds IC (DecIC (p,k)) = (IC p) -' k
let k be Nat; :: thesis: IC (DecIC (p,k)) = (IC p) -' k
dom (Start-At (((IC p) -' k),S)) = {(IC )} by FUNCOP_1:19;
then IC in dom (Start-At (((IC p) -' k),S)) by TARSKI:def 1;
hence IC (DecIC (p,k)) = (Start-At (((IC p) -' k),S)) . (IC ) by FUNCT_4:14
.= (IC p) -' k by FUNCOP_1:87 ;
:: thesis: verum