let s be State of SCMPDS; :: thesis: for P being the Instructions of SCMPDS -valued ManySortedSet of NAT
for I being halt-free Program of SCMPDS
for J being Program of SCMPDS st I c= J & I is_closed_on s,P & I is_halting_on s,P holds
IC (Comput ((P +* J),(Initialize s),(LifeSpan ((P +* (stop I)),(Initialize s))))) = card I
let P be the Instructions of SCMPDS -valued ManySortedSet of NAT ; :: thesis: for I being halt-free Program of SCMPDS
for J being Program of SCMPDS st I c= J & I is_closed_on s,P & I is_halting_on s,P holds
IC (Comput ((P +* J),(Initialize s),(LifeSpan ((P +* (stop I)),(Initialize s))))) = card I
let I be halt-free Program of SCMPDS; :: thesis: for J being Program of SCMPDS st I c= J & I is_closed_on s,P & I is_halting_on s,P holds
IC (Comput ((P +* J),(Initialize s),(LifeSpan ((P +* (stop I)),(Initialize s))))) = card I
let J be Program of SCMPDS; :: thesis: ( I c= J & I is_closed_on s,P & I is_halting_on s,P implies IC (Comput ((P +* J),(Initialize s),(LifeSpan ((P +* (stop I)),(Initialize s))))) = card I )
set s1 = Initialize s;
set P1 = P +* J;
set ss = Initialize s;
set PP = P +* (stop I);
set m = LifeSpan ((P +* (stop I)),(Initialize s));
assume that
A2: I c= J and
A3: I is_closed_on s,P and
A4: I is_halting_on s,P ; :: thesis: IC (Comput ((P +* J),(Initialize s),(LifeSpan ((P +* (stop I)),(Initialize s))))) = card I
NPP (Comput ((P +* J),(Initialize s),(LifeSpan ((P +* (stop I)),(Initialize s))))) = NPP (Comput ((P +* (stop I)),(Initialize s),(LifeSpan ((P +* (stop I)),(Initialize s))))) by A2, A3, A4, Th39;
hence IC (Comput ((P +* J),(Initialize s),(LifeSpan ((P +* (stop I)),(Initialize s))))) = IC (Comput ((P +* (stop I)),(Initialize s),(LifeSpan ((P +* (stop I)),(Initialize s))))) by COMPOS_1:230
.= card I by A3, A4, SCMPDS_6:43 ;
:: thesis: verum