let s be State of SCMPDS ; :: thesis: for I being No-StopCode 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 (s +* (Initialized J))),(s +* (Initialized J)),(LifeSpan (s +* (Initialized (stop I))))) = card I
let I be No-StopCode 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 (s +* (Initialized J))),(s +* (Initialized J)),(LifeSpan (s +* (Initialized (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 (s +* (Initialized J))),(s +* (Initialized J)),(LifeSpan (s +* (Initialized (stop I))))) = card I )
set s1 = s +* (Initialized J);
set ss = s +* (Initialized (stop I));
set m = LifeSpan (s +* (Initialized (stop I)));
assume that
A1: I c= J and
A2: I is_closed_on s and
A3: I is_halting_on s ; :: thesis: IC (Comput (ProgramPart (s +* (Initialized J))),(s +* (Initialized J)),(LifeSpan (s +* (Initialized (stop I))))) = card I
thus IC (Comput (ProgramPart (s +* (Initialized J))),(s +* (Initialized J)),(LifeSpan (s +* (Initialized (stop I))))) = IC (Comput (ProgramPart (s +* (Initialized (stop I)))),(s +* (Initialized (stop I))),(LifeSpan (s +* (Initialized (stop I))))) by A1, A2, A3, Th39, AMI_1:121
.= card I by A2, A3, SCMPDS_6:43 ; :: thesis: verum