:: deftheorem defines `partial1| PDIFF_4:def 4 :
for f being PartFunc of (REAL 3),REAL
for D being set st f is_partial_differentiable`1_on D holds
for b₃ being PartFunc of (REAL 3),REAL holds
( b₃ = f `partial1| D iff ( dom b₃ = D & ( for u being Element of REAL 3 st u in D holds
b₃ . u = partdiff (f,u,1) ) ) );