Proof: $|y|<x \Leftrightarrow -x<y<x$
132971
Prove that $|a| < b \iff -b<a<b$
46613
What's the difference between $\equiv$ and $\leftrightarrow$ in a formal proof?
1932
How to show this equality of $\rho(X,Y)$
33543
is "y1 < x < y2" an inequality or inequalities?
139537
Show that $x\subseteq y \Leftrightarrow \mathcal{P}(x)\subseteq\mathcal{P}(y)$.
43168
Prove that $\limsup\left(b_{n}a_{n}\right)=\limsup\left(a_{n}\right) $ when $\lim_{n\rightarrow\infty}\left(b_{n}\right)=1$
80255
How to prove that $|a-b|<\epsilon$ implies $|b|-\epsilon<|a|<|b|+\epsilon$?
41182
What does the construct x = x || y mean?
35236
Proof $p \vdash q \Rightarrow p$
14158
Prove that $R$ is an integral domain $\Leftrightarrow$ $R[x]$ is an integral domain
147892
Proving if $x<y$ then $\sqrt{x} < \sqrt{y}$
152311
Proving expression$\geq 2$, where variables are $x,y,z$
120911
Clarification on proof: Order of left cosets equal
66247
Proving inequality $\left( \frac {x} {y}\right) ^{x}\left( \frac {1-x} {1-y}\right) ^{1-x}\geqslant 1$
61472
If $0<x<y$, then prove that $\sqrt{x} <\sqrt{y}$ and $x <\sqrt{xy} <y$
125682
Proof verification: the product of two continuous functions is continuous
93102
prove that $f:X\rightarrow Y$ is surjective if and only if $f(f^{-1}(C))=C$