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

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