let s be State of SCM+FSA ; :: thesis: for I, J being Program of SCM+FSA
for a being read-write Int-Location st s . a > 0 & I is_closed_onInit s & I is_halting_onInit s holds
( if>0 a,I,J is_closed_onInit s & if>0 a,I,J is_halting_onInit s )
let I, J be Program of SCM+FSA ; :: thesis: for a being read-write Int-Location st s . a > 0 & I is_closed_onInit s & I is_halting_onInit s holds
( if>0 a,I,J is_closed_onInit s & if>0 a,I,J is_halting_onInit s )
let a be read-write Int-Location ; :: thesis: ( s . a > 0 & I is_closed_onInit s & I is_halting_onInit s implies ( if>0 a,I,J is_closed_onInit s & if>0 a,I,J is_halting_onInit s ) )
set Is = Initialized s;
assume s . a > 0 ; :: thesis: ( not I is_closed_onInit s or not I is_halting_onInit s or ( if>0 a,I,J is_closed_onInit s & if>0 a,I,J is_halting_onInit s ) )
then A1: (Initialized s) . a > 0 by SCMFSA6C:3;
assume I is_closed_onInit s ; :: thesis: ( not I is_halting_onInit s or ( if>0 a,I,J is_closed_onInit s & if>0 a,I,J is_halting_onInit s ) )
then A2: I is_closed_on Initialized s by Th40;
assume I is_halting_onInit s ; :: thesis: ( if>0 a,I,J is_closed_onInit s & if>0 a,I,J is_halting_onInit s )
then I is_halting_on Initialized s by Th41;
then ( if>0 a,I,J is_closed_on Initialized s & if>0 a,I,J is_halting_on Initialized s ) by A1, A2, SCMFSA8B:22;
hence ( if>0 a,I,J is_closed_onInit s & if>0 a,I,J is_halting_onInit s ) by Th40, Th41; :: thesis: verum