let s be State of SCM+FSA ; :: thesis: for a being Int-Location
for I being Program of SCM+FSA st I is parahalting holds
ProperTimesBody a,I,s
let a be Int-Location ; :: thesis: for I being Program of SCM+FSA st I is parahalting holds
ProperTimesBody a,I,s
let I be Program of SCM+FSA ; :: thesis: ( I is parahalting implies ProperTimesBody a,I,s )
assume A1: I is parahalting ; :: thesis: ProperTimesBody a,I,s
then reconsider I9 = I as parahalting Program of SCM+FSA ;
let k be Element of NAT ; :: according to SFMASTR2:def 3 :: thesis: ( k < s . a implies ( I is_closed_on (StepTimes a,I,s) . k & I is_halting_on (StepTimes a,I,s) . k ) )
assume k < s . a ; :: thesis: ( I is_closed_on (StepTimes a,I,s) . k & I is_halting_on (StepTimes a,I,s) . k )
I9 is paraclosed ;
hence I is_closed_on (StepTimes a,I,s) . k by SCMFSA7B:24; :: thesis: I is_halting_on (StepTimes a,I,s) . k
thus I is_halting_on (StepTimes a,I,s) . k by A1, SCMFSA7B:25; :: thesis: verum