let k1, k2 be Integer; :: thesis: for a being Int_position holds not a,k1 >=0_goto k2 is halting
let a be Int_position ; :: thesis: not a,k1 >=0_goto k2 is halting
consider s being State of SCMPDS such that
A1: for d being Int_position holds s . d = - 1 by Th73;
s . (DataLoc (s . a),k1) = - 1 by A1;
then (Exec (a,k1 >=0_goto k2),s) . (IC SCMPDS ) = succ (IC s) by Th69;
hence not a,k1 >=0_goto k2 is halting by Th76; :: thesis: verum