let F be NAT -defined the Instructions of SCM -valued total Function; :: thesis: ( <%(SCM-goto 1)%> ^ <%(halt SCM)%> c= F implies for i1, i2 being Integer
for s being 0 -started State-consisting of 0 ,<*i1*> ^ <*i2*> holds
( F halts_on s & LifeSpan (F,s) = 1 & ( for d being Data-Location holds (Result (F,s)) . d = s . d ) ) )
assume Z: <%(SCM-goto 1)%> ^ <%(halt SCM)%> c= F ; :: thesis: for i1, i2 being Integer
for s being 0 -started State-consisting of 0 ,<*i1*> ^ <*i2*> holds
( F halts_on s & LifeSpan (F,s) = 1 & ( for d being Data-Location holds (Result (F,s)) . d = s . d ) )
let i1, i2 be Integer; :: thesis: for s being 0 -started State-consisting of 0 ,<*i1*> ^ <*i2*> holds
( F halts_on s & LifeSpan (F,s) = 1 & ( for d being Data-Location holds (Result (F,s)) . d = s . d ) )
let s be 0 -started State-consisting of 0 ,<*i1*> ^ <*i2*>; :: thesis: ( F halts_on s & LifeSpan (F,s) = 1 & ( for d being Data-Location holds (Result (F,s)) . d = s . d ) )
set s1 = Comput (F,s,(0 + 1));
A1: ( IC s = 0 & s = Comput (F,s,0) ) by COMPOS_1:def 16, EXTPRO_1:3;
A2: F . 0 = SCM-goto 1 by Z, Th15A;
then A3: IC (Comput (F,s,(0 + 1))) = 0 + 1 by A1, Th23;
A4: F . 1 = halt SCM by Z, Th15A;
hence F halts_on s by A3, EXTPRO_1:31; :: thesis: ( LifeSpan (F,s) = 1 & ( for d being Data-Location holds (Result (F,s)) . d = s . d ) )
thus LifeSpan (F,s) = 1 by A4, A1, A3, EXTPRO_1:34; :: thesis: for d being Data-Location holds (Result (F,s)) . d = s . d
let d be Data-Location ; :: thesis: (Result (F,s)) . d = s . d
thus (Result (F,s)) . d = (Comput (F,s,(0 + 1))) . d by A4, A3, EXTPRO_1:32
.= s . d by A2, A1, Th23 ; :: thesis: verum