:: deftheorem defines internal VECTMETR:def 2 :
for V being non empty MetrStruct holds
( V is internal iff for x, y being Element of V
for p, q being Real st p > 0 & q > 0 holds
ex f being FinSequence of the carrier of V st
( f /. 1 = x & f /. (len f) = y & ( for i being Element of NAT st 1 <= i & i <= (len f) - 1 holds
dist ((f /. i),(f /. (i + 1))) < p ) & ( for F being FinSequence of REAL st len F = (len f) - 1 & ( for i being Element of NAT st 1 <= i & i <= len F holds
F /. i = dist ((f /. i),(f /. (i + 1))) ) holds
|.((dist (x,y)) - (Sum F)).| < q ) ) );