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