let n be Element of NAT ; :: thesis: for X being set
for B being SetSequence of X st B is non-ascending holds
(inferior_setsequence B) . n = (inferior_setsequence B) . (n + 1)
let X be set ; :: thesis: for B being SetSequence of X st B is non-ascending holds
(inferior_setsequence B) . n = (inferior_setsequence B) . (n + 1)
let B be SetSequence of X; :: thesis: ( B is non-ascending implies (inferior_setsequence B) . n = (inferior_setsequence B) . (n + 1) )
assume B is non-ascending ; :: thesis: (inferior_setsequence B) . n = (inferior_setsequence B) . (n + 1)
then ((inferior_setsequence B) . (n + 1)) /\ (B . n) = (inferior_setsequence B) . (n + 1) by Th50, XBOOLE_1:28;
hence (inferior_setsequence B) . n = (inferior_setsequence B) . (n + 1) by Th21; :: thesis: verum