consider f being Function such that
A1: ( dom f = F₁() & ( for x being object st x in F₁() holds
f . x = F₂(x) ) ) from FUNCT_1:sch 3();
reconsider T = f as DecoratedTree by A1, Def8;
take T ; :: thesis: ( dom T = F₁() & ( for p being FinSequence of NAT st p in F₁() holds
T . p = F₂(p) ) )
thus ( dom T = F₁() & ( for p being FinSequence of NAT st p in F₁() holds
T . p = F₂(p) ) ) by A1; :: thesis: verum