let X be set ; :: thesis: for B being SetSequence of X st B is V55() holds

superior_setsequence B = B

let B be SetSequence of X; :: thesis: ( B is V55() implies superior_setsequence B = B )

assume B is V55() ; :: thesis: superior_setsequence B = B

then for n being Nat holds (superior_setsequence B) . n = B . n by Th48;

then for n being Element of NAT holds (superior_setsequence B) . n = B . n ;

hence superior_setsequence B = B by FUNCT_2:63; :: thesis: verum

superior_setsequence B = B

let B be SetSequence of X; :: thesis: ( B is V55() implies superior_setsequence B = B )

assume B is V55() ; :: thesis: superior_setsequence B = B

then for n being Nat holds (superior_setsequence B) . n = B . n by Th48;

then for n being Element of NAT holds (superior_setsequence B) . n = B . n ;

hence superior_setsequence B = B by FUNCT_2:63; :: thesis: verum