let D be non empty set ; :: thesis: for x1, x2, x3, x4, x5, x6, x7, x8, x9, x10 being Element of D holds <*x1,x2,x3,x4,x5*> ^ <*x6,x7,x8,x9,x10*> is Element of 10 -tuples_on D
let x1, x2, x3, x4, x5, x6, x7, x8, x9, x10 be Element of D; :: thesis: <*x1,x2,x3,x4,x5*> ^ <*x6,x7,x8,x9,x10*> is Element of 10 -tuples_on D
reconsider x12345 = <*x1,x2,x3,x4,x5*> as Element of 5 -tuples_on D by LMGSEQ5;
reconsider x67890 = <*x6,x7,x8,x9,x10*> as Element of 5 -tuples_on D by LMGSEQ5;
D c= D ;
hence <*x1,x2,x3,x4,x5*> ^ <*x6,x7,x8,x9,x10*> is Element of 10 -tuples_on D by FINSEQ_2:109; :: thesis: verum