let F be Function of T,R^1; :: thesis: ( F = - f implies F is continuous )

assume A1: F = - f ; :: thesis: F is continuous

consider g being Function of T,R^1 such that

A2: for p being Point of T

for r being Real st f . p = r holds

g . p = - r and

A3: g is continuous by JGRAPH_4:8;

F = g

assume A1: F = - f ; :: thesis: F is continuous

consider g being Function of T,R^1 such that

A2: for p being Point of T

for r being Real st f . p = r holds

g . p = - r and

A3: g is continuous by JGRAPH_4:8;

F = g

proof

hence
F is continuous
by A3; :: thesis: verum
let x be Point of T; :: according to FUNCT_2:def 8 :: thesis: F . x = g . x

thus F . x = - (f . x) by A1, VALUED_1:8

.= g . x by A2 ; :: thesis: verum

end;thus F . x = - (f . x) by A1, VALUED_1:8

.= g . x by A2 ; :: thesis: verum