:: deftheorem Def3 defines C1-curve-like INTEGR1C:def 3 :
for C being PartFunc of REAL,COMPLEX holds
( C is C1-curve-like iff ex a, b being Real ex x, y being PartFunc of REAL,REAL ex Z being Subset of REAL st
( a <= b & [.a,b.] = dom C & [.a,b.] c= dom x & [.a,b.] c= dom y & Z is open & [.a,b.] c= Z & x is_differentiable_on Z & y is_differentiable_on Z & x `| Z is continuous & y `| Z is continuous & C = (x + (<i> (#) y)) | [.a,b.] ) );