let s be State of SCMPDS ; :: thesis: for I being halt-free Program of SCMPDS
for J being Program of SCMPDS st I c= J & I is_closed_on s & I is_halting_on s holds
IC (Comput (ProgramPart ((Initialize s) +* J)),((Initialize s) +* J),(LifeSpan (ProgramPart ((Initialize s) +* (stop I))),((Initialize s) +* (stop I)))) = 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 & I is_halting_on s holds
IC (Comput (ProgramPart ((Initialize s) +* J)),((Initialize s) +* J),(LifeSpan (ProgramPart ((Initialize s) +* (stop I))),((Initialize s) +* (stop I)))) = card I
let J be Program of SCMPDS ; :: thesis: ( I c= J & I is_closed_on s & I is_halting_on s implies IC (Comput (ProgramPart ((Initialize s) +* J)),((Initialize s) +* J),(LifeSpan (ProgramPart ((Initialize s) +* (stop I))),((Initialize s) +* (stop I)))) = card I )
set s1 = (Initialize s) +* J;
set ss = (Initialize s) +* (stop I);
set m = LifeSpan (ProgramPart ((Initialize s) +* (stop I))),((Initialize s) +* (stop I));
I2: (Initialize s) +* (stop I) = s +* (Initialize (stop I)) by SCMPDS_4:5;
assume that
A1: I c= J and
A2: I is_closed_on s and
A3: I is_halting_on s ; :: thesis: IC (Comput (ProgramPart ((Initialize s) +* J)),((Initialize s) +* J),(LifeSpan (ProgramPart ((Initialize s) +* (stop I))),((Initialize s) +* (stop I)))) = card I
thus IC (Comput (ProgramPart ((Initialize s) +* J)),((Initialize s) +* J),(LifeSpan (ProgramPart ((Initialize s) +* (stop I))),((Initialize s) +* (stop I)))) = IC (Comput (ProgramPart ((Initialize s) +* (stop I))),((Initialize s) +* (stop I)),(LifeSpan (ProgramPart ((Initialize s) +* (stop I))),((Initialize s) +* (stop I)))) by A1, A2, A3, Th39, COMPOS_1:24
.= card I by A2, A3, I2, SCMPDS_6:43 ; :: thesis: verum