let s be State of SCMPDS ; :: thesis: for I, J being Program of SCMPDS
for k being Element of NAT st k <= LifeSpan (s +* (Initialized (stop I))) & I c= J & I is_closed_on s & I is_halting_on s holds
IC (Computation (s +* (Initialized J)),k) in dom (stop I)
let I, J be Program of SCMPDS ; :: thesis: for k being Element of NAT st k <= LifeSpan (s +* (Initialized (stop I))) & I c= J & I is_closed_on s & I is_halting_on s holds
IC (Computation (s +* (Initialized J)),k) in dom (stop I)
let k be Element of NAT ; :: thesis: ( k <= LifeSpan (s +* (Initialized (stop I))) & I c= J & I is_closed_on s & I is_halting_on s implies IC (Computation (s +* (Initialized J)),k) in dom (stop I) )
set ss = s +* (Initialized (stop I));
set s1 = Computation (s +* (Initialized J)),k;
set s2 = Computation (s +* (Initialized (stop I))),k;
assume A1: ( k <= LifeSpan (s +* (Initialized (stop I))) & I c= J & I is_closed_on s & I is_halting_on s ) ; :: thesis: IC (Computation (s +* (Initialized J)),k) in dom (stop I)
then IC (Computation (s +* (Initialized J)),k) = IC (Computation (s +* (Initialized (stop I))),k) by Th39, AMI_1:121;
hence IC (Computation (s +* (Initialized J)),k) in dom (stop I) by A1, SCMPDS_6:def 2; :: thesis: verum