let X be set ; :: thesis: for B being SetSequence of X
for n being Nat st B is V55() holds
(inferior_setsequence B) . n = Intersection B
let B be SetSequence of X; :: thesis: for n being Nat st B is V55() holds
(inferior_setsequence B) . n = Intersection B
let n be Nat; :: thesis: ( B is V55() implies (inferior_setsequence B) . n = Intersection B )
defpred S₁[ Nat] means (inferior_setsequence B) . $1 = Intersection B;
assume B is V55() ; :: thesis: (inferior_setsequence B) . n = Intersection B
then A1: for k being Nat st S₁[k] holds
S₁[k + 1] by Th51;
A2: S₁[ 0 ] by Th17;
for k being Nat holds S₁[k] from NAT_1:sch 2(A2, A1);
hence (inferior_setsequence B) . n = Intersection B ; :: thesis: verum