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),(Initialize s),(LifeSpan ((P +* (stop I)),(Initialize s))))) = 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),(Initialize s),(LifeSpan ((P +* (stop I)),(Initialize s))))) = 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),(Initialize s),(LifeSpan ((P +* (stop I)),(Initialize s))))) = 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),(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

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),(Initialize s),(LifeSpan ((P +* (stop I)),(Initialize s))))) = card I

thus 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 A1, A2, A3, Th18

.= card I by A2, A3, SCMPDS_6:29 ; :: thesis: verum

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),(Initialize s),(LifeSpan ((P +* (stop I)),(Initialize s))))) = 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),(Initialize s),(LifeSpan ((P +* (stop I)),(Initialize s))))) = 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),(Initialize s),(LifeSpan ((P +* (stop I)),(Initialize s))))) = 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),(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

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),(Initialize s),(LifeSpan ((P +* (stop I)),(Initialize s))))) = card I

thus 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 A1, A2, A3, Th18

.= card I by A2, A3, SCMPDS_6:29 ; :: thesis: verum