let F be NAT -defined the InstructionsF of SCM -valued total Function; :: thesis: ( <%()%> ^ <%()%> c= F implies for i1, i2 being Integer
for s being 0 -started State-consisting of <%i1,i2%> holds
( F halts_on s & LifeSpan (F,s) = 1 & ( for d being Data-Location holds (Result (F,s)) . d = s . d ) ) )

assume A1: <%()%> ^ <%()%> c= F ; :: thesis: for i1, i2 being Integer
for s being 0 -started State-consisting of <%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 <%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 <%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));
A2: ( IC s = 0 & s = Comput (F,s,0) ) by ;
A3: F . 0 = SCM-goto 1 by ;
then A4: IC (Comput (F,s,(0 + 1))) = 0 + 1 by ;
A5: F . 1 = halt SCM by ;
hence F halts_on s by ; :: thesis: ( LifeSpan (F,s) = 1 & ( for d being Data-Location holds (Result (F,s)) . d = s . d ) )
thus LifeSpan (F,s) = 1 by ; :: 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
.= s . d by A3, A2, Th9 ; :: thesis: verum