let s be State of SCMPDS; :: thesis: for P being Instruction-Sequence of SCMPDS
for I being halt-free Program of
for J being Program of st I c= J & I is_closed_on s,P & I is_halting_on s,P holds
IC (Comput ((P +* J),(),(LifeSpan ((P +* (stop I)),())))) = card I

let P be Instruction-Sequence of SCMPDS; :: thesis: for I being halt-free Program of
for J being Program of st I c= J & I is_closed_on s,P & I is_halting_on s,P holds
IC (Comput ((P +* J),(),(LifeSpan ((P +* (stop I)),())))) = card I

let I be halt-free Program of ; :: thesis: for J being Program of st I c= J & I is_closed_on s,P & I is_halting_on s,P holds
IC (Comput ((P +* J),(),(LifeSpan ((P +* (stop I)),())))) = card I

let J be Program of ; :: thesis: ( I c= J & I is_closed_on s,P & I is_halting_on s,P implies IC (Comput ((P +* J),(),(LifeSpan ((P +* (stop I)),())))) = 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)),());
assume that
A1: I c= J and
A2: I is_closed_on s,P and
A3: I is_halting_on s,P ; :: thesis: IC (Comput ((P +* J),(),(LifeSpan ((P +* (stop I)),())))) = card I
thus IC (Comput ((P +* J),(),(LifeSpan ((P +* (stop I)),())))) = IC (Comput ((P +* (stop I)),(),(LifeSpan ((P +* (stop I)),())))) by A1, A2, A3, Th18
.= card I by ; :: thesis: verum