let n be Nat; :: thesis: for X being set
for B being SetSequence of X st B is non-ascending holds
(superior_setsequence B) . n = B . n
let X be set ; :: thesis: for B being SetSequence of X st B is non-ascending holds
(superior_setsequence B) . n = B . n
let B be SetSequence of X; :: thesis: ( B is non-ascending implies (superior_setsequence B) . n = B . n )
assume B is non-ascending ; :: thesis: (superior_setsequence B) . n = B . n
then ((superior_setsequence B) . (n + 1)) \/ (B . n) = B . n by Th47, XBOOLE_1:12;
hence (superior_setsequence B) . n = B . n by Th22; :: thesis: verum