let P be the Instructions of SCMPDS -valued ManySortedSet of NAT ; :: thesis: for I, J being Program of SCMPDS
for s being State of SCMPDS
for k being Element of NAT st I is_closed_on s,P & I is_halting_on s,P & k < LifeSpan ((P +* (stop I)),(Initialize s)) holds
CurInstr ((P +* (stop (I ';' J))),(Comput ((P +* (stop (I ';' J))),(Initialize s),k))) <> halt SCMPDS
let I, J be Program of SCMPDS; :: thesis: for s being State of SCMPDS
for k being Element of NAT st I is_closed_on s,P & I is_halting_on s,P & k < LifeSpan ((P +* (stop I)),(Initialize s)) holds
CurInstr ((P +* (stop (I ';' J))),(Comput ((P +* (stop (I ';' J))),(Initialize s),k))) <> halt SCMPDS
let s be State of SCMPDS; :: thesis: for k being Element of NAT st I is_closed_on s,P & I is_halting_on s,P & k < LifeSpan ((P +* (stop I)),(Initialize s)) holds
CurInstr ((P +* (stop (I ';' J))),(Comput ((P +* (stop (I ';' J))),(Initialize s),k))) <> halt SCMPDS
let k be Element of NAT ; :: thesis: ( I is_closed_on s,P & I is_halting_on s,P & k < LifeSpan ((P +* (stop I)),(Initialize s)) implies CurInstr ((P +* (stop (I ';' J))),(Comput ((P +* (stop (I ';' J))),(Initialize s),k))) <> halt SCMPDS )
set s1 = Initialize s;
set P1 = P +* (stop I);
set s2 = Initialize s;
set P2 = P +* (stop (I ';' J));
set m = LifeSpan ((P +* (stop I)),(Initialize s));
set s3 = Comput ((P +* (stop (I ';' J))),(Initialize s),k);
set P3 = P +* (stop (I ';' J));
assume that
A1: I is_closed_on s,P and
A2: I is_halting_on s,P and
A3: k < LifeSpan ((P +* (stop I)),(Initialize s)) ; :: thesis: CurInstr ((P +* (stop (I ';' J))),(Comput ((P +* (stop (I ';' J))),(Initialize s),k))) <> halt SCMPDS
assume CurInstr ((P +* (stop (I ';' J))),(Comput ((P +* (stop (I ';' J))),(Initialize s),k))) = halt SCMPDS ; :: thesis: contradiction
then A5: CurInstr ((P +* (stop I)),(Comput ((P +* (stop I)),(Initialize s),k))) = halt SCMPDS by A1, A2, A3, SCMPDS_6:41;
P +* (stop I) halts_on Initialize s by A2, SCMPDS_6:def 3;
hence contradiction by A3, A5, EXTPRO_1:def 14; :: thesis: verum