let p be FinSequence of X; :: thesis: p is non-empty
let x be object ; :: according to FUNCT_1:def 9 :: thesis: ( not x in proj1 p or not p . x is empty )
assume x in dom p ; :: thesis: not p . x is empty
then p . x in rng p by FUNCT_1:def 3;
hence not p . x is empty ; :: thesis: verum