Section Precision.
Variables (K : ordType) (V : Type) (U : union_map_class K V).
Implicit Types (x y : U).

Lemma prec_filtV x1 x2 y1 y2 :
valid (x1 \+ y1) -> x1 \+ y1 = x2 \+ y2 ->
reflect (x1 = um_filter (mem (dom x1)) x2) (valid (x1 \+ y2)).