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 = Initialize 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: (Initialize 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 Initialize 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 Initialize s by Th41;
then ( if=0 a,I,J is_closed_on Initialize s & if=0 a,I,J is_halting_on Initialize s ) by A1, A2, SCMFSA8B:16;
hence ( if=0 a,I,J is_closed_onInit s & if=0 a,I,J is_halting_onInit s ) by Th40, Th41; :: thesis: verum