let p, q be Element of REAL 3; :: thesis: for f1, f2, f3, g1, g2, g3 being PartFunc of ,
for t1, t2 being Real st p = (VFunc f1,f2,f3) . t1 & q = (VFunc g1,g2,g3) . t2 holds
len (p - q) = 3
let f1, f2, f3, g1, g2, g3 be PartFunc of ,; :: thesis: for t1, t2 being Real st p = (VFunc f1,f2,f3) . t1 & q = (VFunc g1,g2,g3) . t2 holds
len (p - q) = 3
let t1, t2 be Real; :: thesis: ( p = (VFunc f1,f2,f3) . t1 & q = (VFunc g1,g2,g3) . t2 implies len (p - q) = 3 )
assume ( p = (VFunc f1,f2,f3) . t1 & q = (VFunc g1,g2,g3) . t2 ) ; :: thesis: len (p - q) = 3
then p - q = |[((f1 . t1) - (g1 . t2)),((f2 . t1) - (g2 . t2)),((f3 . t1) - (g3 . t2))]| by Th49;
hence len (p - q) = 3 by FINSEQ_1:62; :: thesis: verum