let n be Nat; :: thesis: for X being set

for B being SetSequence of X st B is V56() holds

(inferior_setsequence B) . n = B . n

let X be set ; :: thesis: for B being SetSequence of X st B is V56() holds

(inferior_setsequence B) . n = B . n

let B be SetSequence of X; :: thesis: ( B is V56() implies (inferior_setsequence B) . n = B . n )

assume B is V56() ; :: thesis: (inferior_setsequence B) . n = B . n

then ((inferior_setsequence B) . (n + 1)) /\ (B . n) = B . n by Th44, XBOOLE_1:28;

hence (inferior_setsequence B) . n = B . n by Th21; :: thesis: verum

for B being SetSequence of X st B is V56() holds

(inferior_setsequence B) . n = B . n

let X be set ; :: thesis: for B being SetSequence of X st B is V56() holds

(inferior_setsequence B) . n = B . n

let B be SetSequence of X; :: thesis: ( B is V56() implies (inferior_setsequence B) . n = B . n )

assume B is V56() ; :: thesis: (inferior_setsequence B) . n = B . n

then ((inferior_setsequence B) . (n + 1)) /\ (B . n) = B . n by Th44, XBOOLE_1:28;

hence (inferior_setsequence B) . n = B . n by Th21; :: thesis: verum