let n be Nat; :: thesis: for X being set
for Si being SigmaField of X
for XSeq being SetSequence of Si
for x being object holds
( x in (Partial_Intersection XSeq) . n iff for k being Nat st k <= n holds
x in XSeq . k )
let X be set ; :: thesis: for Si being SigmaField of X
for XSeq being SetSequence of Si
for x being object holds
( x in (Partial_Intersection XSeq) . n iff for k being Nat st k <= n holds
x in XSeq . k )
let Si be SigmaField of X; :: thesis: for XSeq being SetSequence of Si
for x being object holds
( x in (Partial_Intersection XSeq) . n iff for k being Nat st k <= n holds
x in XSeq . k )
let XSeq be SetSequence of Si; :: thesis: for x being object holds
( x in (Partial_Intersection XSeq) . n iff for k being Nat st k <= n holds
x in XSeq . k )
reconsider XSeq = XSeq as SetSequence of X ;
let x be object ; :: thesis: ( x in (Partial_Intersection XSeq) . n iff for k being Nat st k <= n holds
x in XSeq . k )
( x in (Partial_Intersection XSeq) . n iff for k being Nat st k <= n holds
x in XSeq . k ) by Th12;
hence ( x in (Partial_Intersection XSeq) . n iff for k being Nat st k <= n holds
x in XSeq . k ) ; :: thesis: verum