let a be Int_position; :: thesis: for l being Element of NAT

for k1 being Integer holds NIC ((a := k1),l) = {(l + 1)}

let l be Element of NAT ; :: thesis: for k1 being Integer holds NIC ((a := k1),l) = {(l + 1)}

let k1 be Integer; :: thesis: NIC ((a := k1),l) = {(l + 1)}

set i = a := k1;

for s being State of SCMPDS st IC s = l holds

(Exec ((a := k1),s)) . (IC ) = (IC s) + 1 by SCMPDS_2:45;

hence NIC ((a := k1),l) = {(l + 1)} by Th1; :: thesis: verum

for k1 being Integer holds NIC ((a := k1),l) = {(l + 1)}

let l be Element of NAT ; :: thesis: for k1 being Integer holds NIC ((a := k1),l) = {(l + 1)}

let k1 be Integer; :: thesis: NIC ((a := k1),l) = {(l + 1)}

set i = a := k1;

for s being State of SCMPDS st IC s = l holds

(Exec ((a := k1),s)) . (IC ) = (IC s) + 1 by SCMPDS_2:45;

hence NIC ((a := k1),l) = {(l + 1)} by Th1; :: thesis: verum