let n be Nat; :: thesis: for seq being Real_Sequence st seq is V55() & seq is V96() holds
(inferior_realsequence seq) . n = (inferior_realsequence seq) . (n + 1)
let seq be Real_Sequence; :: thesis: ( seq is V55() & seq is V96() implies (inferior_realsequence seq) . n = (inferior_realsequence seq) . (n + 1) )
assume A1: ( seq is V55() & seq is V96() ) ; :: thesis: (inferior_realsequence seq) . n = (inferior_realsequence seq) . (n + 1)
then (inferior_realsequence seq) . (n + 1) <= seq . n by Th71;
then min (((inferior_realsequence seq) . (n + 1)),(seq . n)) = (inferior_realsequence seq) . (n + 1) by XXREAL_0:def 9;
hence (inferior_realsequence seq) . n = (inferior_realsequence seq) . (n + 1) by A1, Th46; :: thesis: verum