All proof directives can be included using the proof:kind pattern, where the proof directives are shown in Table 1. A plain proof can also be written without a kind, as {proof}. The directive is enumerated by default and can take in an optional title argument which is shown in brackets after the proof.
Same as Sphinx Proof 🎉
The implementation and documentation for proofs, theorems, etc. is based on Sphinx Proof, the syntax can be used interchangeably. We have reused the examples in that extension here to show off the various parts of the MyST extension.
Changes to the original extension include being able to click on the proof label (e.g. “Theorem 1”), and having a link to that proof anchor. We have also updated the styles from both Sphinx and Jupyter Book to be more distinct from admonitions.
A plain proof does not need a kind prefix at all — use {proof}.
You can also reference proofs with any cross-reference syntax (including the {proof:ref} role). We recommend the Markdown link syntax.
Here is an example of a {proof:theorem} with a custom title:
proof:theorem - Unknown Directive
proof:theorem - Unknown Directive:label: my-theorem
Given $y \in \mathbb R^n$ and linear subspace $S \subset \mathbb R^n$,
there exists a unique solution to the minimization problem
```{math}
\hat y := \argmin_{z \in S} \|y - z\|
```
The minimizer $\hat y$ is the unique vector in $\mathbb R^n$ that satisfies
- $\hat y \in S$
- $y - \hat y \perp S$
The vector $\hat y$ is called the **orthogonal projection** of $y$ onto $S$.Table 1:Proof kinds that can be used as directives
|
|
|
|
|
|
|
|
|
|
|
|
|
|
proof directive¶
Alias: prf:proof, proof:proof, prf:axiom, proof:axiom, prf:lemma, proof:lemma, prf:definition, proof:definition, prf:criterion, proof:criterion, prf:remark, proof:remark, prf:conjecture, proof:conjecture, prf:corollary, proof:corollary, prf:algorithm, proof:algorithm, prf:example, proof:example, prf:property, proof:property, prf:observation, proof:observation, prf:proposition, proof:proposition, prf:assumption, proof:assumption, prf:theorem, proof:theorem
- Directive Argument (parsed)
- No description
- Directive Body (parsed, required)
- No description
- Options
- class (string)
Annotate the proof with a set of space-delimited class names.
- label (string)
Label the proof to be cross-referenced or explicitly linked to.
- Alias:
name - enumerated (boolean)
Turn on/off the numbering for the specific proof
- Alias:
numbered - enumerator (string)
Explicitly set the proof number
- Alias:
number - nonumber (boolean)
Legacy flag to disable numbering of proofs; equivalent to
enumerated: false
Referencing Proofs¶
You can refer to a proof using the standard link syntax:
[{name}](#my-theorem)creates {name}[{number}](#my-theorem)creates {number}[See Theorem](#my-theorem)creates See Theorem
Compatibility with Sphinx Proof
You may also use the {proof:ref} role like: {proof:ref}`my-theorem`, which will replace the reference with the theorem number like so: my-theorem. When an explicit text is provided, this caption will serve as the title of the reference. For example, {proof:ref}`Orthogonal-Projection-Theorem <my-theorem>` will produce: Orthogonal-Projection-Theorem <my-theorem>.
Hiding Proof Content¶
To hide the directive, simply add :class: dropdown as a directive option.
Example
Proof Examples¶
Proofs¶
Source: Adapted from QuantEcon
Theorems¶
Source: QuantEcon
Axioms¶
Source: Stachurski (2009)
Lemmas¶
Source: QuantEcon
Definitions¶
Source: QuantEcon
Criteria¶
Source: Wikipedia
Remarks¶
Source: QuantEcon
Conjectures¶
Corollaries¶
Source: QuantEcon
Algorithms¶
Source: Wikipedia
Examples¶
Source: QuantEcon
Properties¶
Observations¶
Propositions¶
Assumptions¶
- Stachurski, J. (2009). Economic Dynamics: Theory and Computation (Vol. 1). The MIT Press. https://ideas.repec.org/b/mtp/titles/0262012774.html
