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 & J is_closed_onInit s & J 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 & J is_closed_onInit s & J 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 & J is_closed_onInit s & J 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 J is_closed_onInit s or not J 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 J is_closed_onInit s ; :: thesis: ( not J 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: J is_closed_on Initialized s by Th40;
assume J is_halting_onInit s ; :: thesis: ( if>0 (a,I,J) is_closed_onInit s & if>0 (a,I,J) is_halting_onInit s )
then J 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:24;
hence ( if>0 (a,I,J) is_closed_onInit s & if>0 (a,I,J) is_halting_onInit s ) by Th40, Th41; :: thesis: verum