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Proof Builder Help

Quick Start

1. Add a theorem title and statement at the top.
2. All inputs are plain text by default.
3. Use `$...$` for inline math and `$$...$$` or `\[...\]` for display math.
4. Proof lines can mix prose, inline math, and display equations in the same field.
5. Use `Enter` for a newline, `Cmd/Ctrl+Shift+Enter` to add and focus a proof line below, and `Tab` / `Shift+Tab` to indent or outdent.

Editing Workflow

1. Drag any line by the row handle area, or use Up/Down buttons.
2. Use Duplicate and Add Below to draft variants quickly.
3. Use the right sidebar snippets for limits, integrals, summations, and symbols.
4. Insert proof templates like Modus Ponens, contradiction, induction, and case split.

Export & Share

1. Copy output as Markdown, plain text, or LaTeX from the toolbar.
2. Use Embed to generate an embeddable version of the current proof.
3. Start a session only when you want collaborative or persisted workflow state.

Example Proofs

Modus Ponens

Logic

From P and P -> Q, conclude Q.

Theorem:

Irrationality of sqrt(2)

Number Theory

Classic contradiction proof.

Theorem:

Limit of x^2 at 2

Real Analysis

Epsilon-delta proof that lim_{x->2} x^2 = 4.

Theorem:

Kernel is a Subspace

Linear Algebra

Show ker(T) is a subspace of V.

Theorem:

Sum of First n Integers

Combinatorics

Induction proof for 1+...+n = n(n+1)/2.

Theorem:

De Morgan's Law

Set Theory

Show (A \cup B)^c = A^c \cap B^c by double inclusion.

Theorem:

Triangle Inequality in R

Metric Spaces

Derive |a+b| \le |a|+|b| from squaring.

Theorem:

Uniqueness of Identity

Abstract Algebra

If a group has identity elements e and e', then e=e'.

Theorem: