Show that $ xz \leq yz $ $ \land$ $ z > 0 $ $ \implies x \leq y $
12954
Prove if $ac>bc$ and $c>0$, then $a>b$
127397
$z\overline{w}\ne 1 $ Prove that $|\frac{w-z}{1-\overline{w}z}|\le 1|$ if $|z|\le 1$ and $|w|\le 1 $
95293
Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$
125707
A simple proof (hopefully) for $2^x \neq 0$
87567
How to prove $1+x \leq e^x~\forall x \in \mathbb{R}?$
10540
Prove $\vdash \neg(\square F\land p)$ in $KD$
26302
Prove that $(X \cap Y) \cup Z = (X \cup Z) \cap (Y \cup Z)$
138632
Proof that if $a > 0$, then $\frac{1}{a} > 0$ using just field and order axioms
62239
For a polynomial $p(z)$, prove there exist $R>0$, such that if $|z|=R$, then $|p(z)|\geq |a_n|R^n/2$
27901
Proving $\sum\limits_{i=1}^k | \langle x,v_i \rangle \langle y,v_i\rangle| \leq \|x\|\cdot \|y\|$
54380
Prove if $|z| < 1$ and $ |w| < 1$, then $|1-zw^*| \neq 0$ and $| {{z-w} \over {1-zw^*}}| < 1$
39514
how do I prove that $1 > 0$ in an ordered field?
20626
Prove that $x^y < y^x$
99927
The closure of $\{ z:|f(z)|<c\}$ is the set $\{z:|f(z)|\leq c\}$.
142631
Show that A has the same cardinality as $A\setminus\{x,y,z\}$
64955
Show that there are $ a,b \geq 0 $ so that $ |f(x)| \leq ax+b, \forall x \geq 0.$
76148
Show that $\exists c \in \mathbb{R} : f(c) = 0$