let s be All-State of SumTuring ; :: thesis: for p, h, t being set st s = [p,h,t] & p <> 5 holds
Following s = [((TRAN s) `1 ),((Head s) + (offset (TRAN s))),(Tape-Chg (s `3 ),(Head s),((TRAN s) `2 ))]
let p, h, t be set ; :: thesis: ( s = [p,h,t] & p <> 5 implies Following s = [((TRAN s) `1 ),((Head s) + (offset (TRAN s))),(Tape-Chg (s `3 ),(Head s),((TRAN s) `2 ))] )
assume A1: ( s = [p,h,t] & p <> 5 ) ; :: thesis: Following s = [((TRAN s) `1 ),((Head s) + (offset (TRAN s))),(Tape-Chg (s `3 ),(Head s),((TRAN s) `2 ))]
5 = the AcceptS of SumTuring by Def15;
hence Following s = [((TRAN s) `1 ),((Head s) + (offset (TRAN s))),(Tape-Chg (s `3 ),(Head s),((TRAN s) `2 ))] by A1, Th29; :: thesis: verum