let X be set ; :: thesis: for B being SetSequence of X st B is non-descending holds
inferior_setsequence B = B
let B be SetSequence of X; :: thesis: ( B is non-descending implies inferior_setsequence B = B )
assume B is non-descending ; :: thesis: inferior_setsequence B = B
then for n being Nat holds (inferior_setsequence B) . n = B . n by Th45;
then for n being Element of NAT holds (inferior_setsequence B) . n = B . n ;
hence inferior_setsequence B = B by FUNCT_2:63; :: thesis: verum