let i1, i2 be Integer; :: thesis: for s being State-consisting of 0 , 0 , 0 ,<%((dl. 0 ) >0_goto 1)%> ^ <%(halt SCM )%>,<*i1*> ^ <*i2*> holds
( ProgramPart s halts_on s & LifeSpan (ProgramPart s),s = 1 & ( for d being Data-Location holds (Result (ProgramPart s),s) . d = s . d ) )
let s be State-consisting of 0 , 0 , 0 ,<%((dl. 0 ) >0_goto 1)%> ^ <%(halt SCM )%>,<*i1*> ^ <*i2*>; :: thesis: ( ProgramPart s halts_on s & LifeSpan (ProgramPart s),s = 1 & ( for d being Data-Location holds (Result (ProgramPart s),s) . d = s . d ) )
set s1 = Comput (ProgramPart s),s,(0 + 1);
A1: s . 0 = (dl. 0 ) >0_goto 1 by Th15;
A2: s . 1 = halt SCM by Th15;
A3: ( IC s = 0 & s = Comput (ProgramPart s),s,0 ) by Th15, AMI_1:13;
s . (dl. 0 ) = i1 by Th15;
then A4: IC (Comput (ProgramPart s),s,(0 + 1)) = 0 + 1 by A1, A3, Th25;
hence ProgramPart s halts_on s by A2, Th3; :: thesis: ( LifeSpan (ProgramPart s),s = 1 & ( for d being Data-Location holds (Result (ProgramPart s),s) . d = s . d ) )
thus LifeSpan (ProgramPart s),s = 1 by A2, A3, A4, Th17; :: thesis: for d being Data-Location holds (Result (ProgramPart s),s) . d = s . d
let d be Data-Location ; :: thesis: (Result (ProgramPart s),s) . d = s . d
thus (Result (ProgramPart s),s) . d = (Comput (ProgramPart s),s,(0 + 1)) . d by A2, A4, Th4
.= s . d by A1, A3, Th25 ; :: thesis: verum