let n be Element of NAT ; :: thesis: for X being set
for B being SetSequence of X st B is non-descending holds
(superior_setsequence B) . n = Union B
let X be set ; :: thesis: for B being SetSequence of X st B is non-descending holds
(superior_setsequence B) . n = Union B
let B be SetSequence of X; :: thesis: ( B is non-descending implies (superior_setsequence B) . n = Union B )
defpred S₁[ Nat] means (superior_setsequence B) . $1 = Union B;
assume B is non-descending ; :: thesis: (superior_setsequence B) . n = Union B
then A1: for k being Element of NAT st S₁[k] holds
S₁[k + 1] by Th41;
A2: S₁[ 0 ] by Th18;
for k being Element of NAT holds S₁[k] from NAT_1:sch 1(A2, A1);
hence (superior_setsequence B) . n = Union B ; :: thesis: verum