if |f| is periodic then f is periodic
33489
|f| is periodic implies f is periodic
47135
Prove if a = b, then f(a) = f(b) for any function f (with natural deduction)
72694
Proving that $f(x) = g(x)$ for some $x \in [a,b]$ if $f,g$ continuous, $f(a)  g(b)$
91980
Prove that f is one-to-one on D
42075
If $f$ is analytic then $|f|$ is not constant unless $f$ is constant
21391
Proving Functions are Surjective
83713
If $z,w\in \mathbb{C}^{\times}$, then $|z+w|=|z|+|w|$ iff $w=tz$ for some $t\gt 0$
104757
If $f \circ g$ is surjective, then f is surjective
76790
Condition to guarantee $f=0$ on $[a,b]$
64650
If $a\operatorname{Re}(f(z))+b\operatorname{Im}(f(z))=c$ then f is constant
133266
If $(X, \mathcal{T})$ has a countable subbasis, then it has a countable basis
34836
Composition of Absolutely Continuous Functions
157715
Proving $f$ is Lebesgue integrable iff $|f|$ is Lebesgue integrable.
28399
Showing $f$ is constant
61640
Prove c exists for f:[0,1] -> R
78472
Sequence is periodic $x_{n+2}=|x_{n+1}-x_{n-1}|$
83461
Continuous iff composition with every linear functional is continuous