**(Prove It)****(Yes You Can)**

**(Prove It)**

**(Yes You Can)**

Welcome to **Prooftoys**, an online tool for exploring mathematical
reasoning and website with resources for learning. The overriding
design objective of Prooftoys is to *drastically reduce the learning
curve* for working with precise, automated reasoning. Here you can:

- Introduce yourself to basic
**logic concepts**through pictures. - Get acquainted with
**the automated logic**used here. **Dig into proofs**created and verified by Prooftoys. Understand in detail or just browse.- Eventually you may experiment with
**building your own**proofs with the online tool.

The core of the system is proudly free and open source software, hosted on GitHub.

## Logic through pictures

This site has explanations of concepts at work in mathematical
logic and the Prooftoys system, with **interactive pictures** resembling these:

## The automated logic

Prooftoys applies the kind of logic used in several popular tools for specialists, but presents it with the overriding goal of being as approachable to beginners as possible, and to make statements in the language familiar to users of ordinary math textbooks. Next steps in this direction -

**Concepts**of the Prooftoys logic.- The logical
**language**of Prooftoys. - The
**rules of the game**as played with Prooftoys.

## Digging into proofs

With Prooftoys you can *view and study completed proofs*. This
website contains “live” displays of many of them, like this:

Some are proofs of basic facts about *numbers*, derived from classic
axioms. Others are useful theorems of *pure logic* that can apply to
any field of math. You can view the facts and their proofs, which are
all worked out rigorously and computer-verified. If a step is not
clear, you can “drill down” into the details, all the way down to the
most basic axioms and inferences.

- Proved facts about
**the real numbers**. - Key theorems of
**pure logic**.

## Building your own

- The more finished version of the proof builder is targeted for solving simple equations, at the companion Mathtoys site.
- For the boldest, dive into
*building your own proofs*with the**proof builder**. This tool has some rough edges still, though it will only do correct inferences.