let p be Instruction-Sequence of SCM+FSA; :: thesis: for s being State of SCM+FSA
for a being read-write Int-Location
for I being parahalting Program of SCM+FSA holds ProperBodyWhile=0 a,I,s,p
let s be State of SCM+FSA; :: thesis: for a being read-write Int-Location
for I being parahalting Program of SCM+FSA holds ProperBodyWhile=0 a,I,s,p
let a be read-write Int-Location ; :: thesis: for I being parahalting Program of SCM+FSA holds ProperBodyWhile=0 a,I,s,p
let I be parahalting Program of SCM+FSA; :: thesis: ProperBodyWhile=0 a,I,s,p
let k be Element of NAT ; :: according to SCMFSA9A:def 1 :: thesis: ( ((StepWhile=0 (a,I,p,s)) . k) . a = 0 implies ( I is_closed_on (StepWhile=0 (a,I,p,s)) . k,p +* (while=0 (a,I)) & I is_halting_on (StepWhile=0 (a,I,p,s)) . k,p +* (while=0 (a,I)) ) )
assume ((StepWhile=0 (a,I,p,s)) . k) . a = 0 ; :: thesis: ( I is_closed_on (StepWhile=0 (a,I,p,s)) . k,p +* (while=0 (a,I)) & I is_halting_on (StepWhile=0 (a,I,p,s)) . k,p +* (while=0 (a,I)) )
thus I is_closed_on (StepWhile=0 (a,I,p,s)) . k,p +* (while=0 (a,I)) by SCMFSA7B:18; :: thesis: I is_halting_on (StepWhile=0 (a,I,p,s)) . k,p +* (while=0 (a,I))
thus I is_halting_on (StepWhile=0 (a,I,p,s)) . k,p +* (while=0 (a,I)) by SCMFSA7B:19; :: thesis: verum