Formal statements

Labeled formal units asserted in the argument — theorems, proofs, definitions, and the definitional structures.

<corollary>

Specification

category theorem-family · eHTML <corollary> · JATS <statement> · content structured → <children>

attribute	kind	values / default	notes
`name`	kwarg		Optional name suffix for the corollary’s label, parallel to <theorem>’s `name` kwarg.
`+numbered` / `-numbered`	flag	default on	Whether this corollary participates in the propositional theorem-family shared counter.

Produced by: canonical <corollary>.

Examples


<corollary | Every prime greater than 2 is odd.>

Corollary 1.

Every prime greater than 2 is odd.

Minipage 81.

<corollary #cor:bounded>
Any continuous function on a closed interval is bounded.
</corollary>

Corollary 1.

Any continuous function on a closed interval is bounded.

Minipage 82.

<dd>

Specification

category block-prose · eHTML <dd> · JATS <def> · content structured → <children>

No kwargs or boolean flags.

Produced by: canonical <dd>.

Examples


<dd | An academic publishing system built on HTML+CSS+JS.>

An academic publishing system built on HTML+CSS+JS.

Minipage 83.

A definition-list description. Appears as a child of <dl>, following the term it defines.

<dd |
A multi-paragraph definition.

The second paragraph of the definition.
>

A multi-paragraph definition.

The second paragraph of the definition.

Minipage 84.

Multi-paragraph descriptions are valid — the pipe content’s paragraph structure is preserved.

<definition>

Specification

category theorem-family · eHTML <definition> · JATS <statement> · content structured → <children>

attribute	kind	values / default	notes
`name`	kwarg		Optional name suffix for the definition’s label.
`+numbered` / `-numbered`	flag	default on	Whether this definition participates in the definition counter.

Produced by: canonical <definition>.

Examples


<definition | A *group* is a set with an associative binary operation, identity, and inverses.>

Definition 1.

A group is a set with an associative binary operation, identity, and inverses.

Minipage 85.

<definition name="Group" #def:group>
A *group* is a set $G$ together with a binary operation
$\cdot$ satisfying associativity, identity, and inverses.
</definition>

Definition 1 (Group).

A group is a set $G$ together with a binary operation $\cdot$ satisfying associativity, identity, and inverses.

Minipage 86.

<dl>

Specification

category block-prose · eHTML <dl> · JATS <def-list> · content empty → <children>

No kwargs or boolean flags.

Produced by: canonical <dl>.

Examples

<dl>
  <dt | enscribe>
  <dd | An academic publishing system built on HTML+CSS+JS.>
  <dt | eHTML>
  <dd | The canonical semantic HTML vocabulary.>
  <dt | Enscribe shorthand>
  <dd | The shorthand authoring syntax that compiles to eHTML.>
</dl>

enscribe: An academic publishing system built on HTML+CSS+JS.
eHTML: The canonical semantic HTML vocabulary.
Enscribe shorthand: The shorthand authoring syntax that compiles to eHTML.

Minipage 87.

Long-form <dl> with short-form <dt>/<dd> children. The natural authoring pattern.

<dl .compact>
  <dt | term-1>
  <dd | First definition of term-1.>
  <dd | Second definition of term-1.>
</dl>

term-1: First definition of term-1.; Second definition of term-1.

Minipage 88.

One term with multiple definitions — a valid HTML pattern.

<dt>

Specification

category block-prose · eHTML <dt> · JATS <term> · content prose → <children>

No kwargs or boolean flags.

Produced by: canonical <dt>.

Examples


<dt | enscribe>

enscribe

Minipage 89.

A definition-list term. Appears as a child of <dl>.

<dt | <code | strict-mode>>

strict-mode

Minipage 90.

Inline markup in a term. The recursive-content pass parses the pipe content normally.

<example>

Specification

category theorem-family · eHTML <example> · JATS <statement> · content structured → <children>

attribute	kind	values / default	notes
`name`	kwarg		Optional name suffix for the example’s label.
`+numbered` / `-numbered`	flag	default on	Whether this example participates in the example counter.

Produced by: canonical <example>.

Examples


<example | The integers under addition form a group.>

Example 1.

The integers under addition form a group.

Minipage 91.

<example #ex:integers>
The integers $\mathbb{Z}$ under addition form a group: the
operation is associative, $0$ is the identity, and every
integer has an additive inverse.
</example>

Example 1.

The integers $Z$ under addition form a group: the operation is associative, $0$ is the identity, and every integer has an additive inverse.

Minipage 92.

<glossary>

Specification

category block-prose · eHTML <glossary> · JATS <glossary> · content empty → <children>

No kwargs or boolean flags.

Produced by: canonical <glossary>.

Examples

<glossary #project-terms>
  <glossary-entry>
    <dt | enscribe>
    <dd | An academic publishing system built on HTML+CSS+JS.>
  </glossary-entry>
  <glossary-entry>
    <dt | eHTML>
    <dd | The canonical semantic HTML vocabulary.>
  </glossary-entry>
</glossary>

enscribe

An academic publishing system built on HTML+CSS+JS.

eHTML

The canonical semantic HTML vocabulary.

Minipage 93.

A glossary with two entries. Each <glossary-entry> uses <dt>/<dd> for its term and definition (the same shapes <dl> uses), wrapped in the entry’s own envelope for cross-reference / styling.

<glossary-entry>

Specification

category block-prose · eHTML <glossary-entry> · JATS <def-item> · content empty → <children>

No kwargs or boolean flags.

Produced by: canonical <glossary-entry>.

Examples

<glossary-entry #term:enscribe>
  <dt | enscribe>
  <dd | An academic publishing system built on HTML+CSS+JS.>
</glossary-entry>

enscribe

An academic publishing system built on HTML+CSS+JS.

Minipage 94.

A single glossary entry. The id uses the “term:” colon-prefix convention so cross-references like <ref @term:enscribe> can resolve into the entry.

<lemma>

Specification

category theorem-family · eHTML <lemma> · JATS <statement> · content structured → <children>

attribute	kind	values / default	notes
`name`	kwarg		Optional name suffix for the lemma’s label, parallel to <theorem>’s `name` kwarg.
`+numbered` / `-numbered`	flag	default on	Whether this lemma participates in the propositional theorem- family shared counter.

Produced by: canonical <lemma>.

Examples


<lemma | Every continuous function on a compact set attains its maximum.>

Lemma 1.

Every continuous function on a compact set attains its maximum.

Minipage 95.

<lemma name="Zorn" #lem:zorn>
Every non-empty partially-ordered set in which every chain has
an upper bound contains a maximal element.
</lemma>

Lemma 1 (Zorn).

Every non-empty partially-ordered set in which every chain has an upper bound contains a maximal element.

Minipage 96.

<proof>

Specification

category theorem-family · eHTML <proof> · JATS <statement> · content structured → <children>

attribute	kind	values / default	notes
`name`	kwarg		Optional name suffix — e.g.
`+numbered` / `-numbered`	flag	default off	Whether this proof is numbered.

Produced by: canonical <proof>.

Examples

<theorem | The sum of two even integers is even.>

<proof>
Let $a = 2m$ and $b = 2n$. Then $a + b = 2(m + n)$, which is
even. $\square$
</proof>

Theorem 1.

The sum of two even integers is even.

Proof.

Let $a = 2 m$ and $b = 2 n$ . Then $a + b = 2 (m + n)$ , which is even. $□$

Minipage 97.

The canonical pattern: <theorem> followed by sibling <proof>. The proof is NOT nested inside the theorem.

<proof name="of Theorem 1.2">
The argument follows from the preceding lemma.
</proof>

Proof.

The argument follows from the preceding lemma.

Minipage 98.

Optional name kwarg lets the proof identify what it proves (useful when the proof is separated from its theorem by intervening text).

<proposition>

Specification

category theorem-family · eHTML <proposition> · JATS <statement> · content structured → <children>

attribute	kind	values / default	notes
`name`	kwarg		Optional name suffix for the proposition’s label.
`+numbered` / `-numbered`	flag	default on	Whether this proposition participates in the propositional theorem-family shared counter.

Produced by: canonical <proposition>.

Examples


<proposition | The sum of two even integers is even.>

Proposition 1.

The sum of two even integers is even.

Minipage 99.

<proposition name="Cauchy-Schwarz">
For any vectors $u$, $v$ in an inner-product space,
$|\langle u, v \rangle| \le \|u\| \, \|v\|$.
</proposition>

Proposition 1 (Cauchy-Schwarz).

For any vectors $u$ , $v$ in an inner-product space, $∣ ⟨ u, v ⟩ ∣ \leq ∥ u ∥ ∥ v ∥$ .

Minipage 100.

<remark>

Specification

category theorem-family · eHTML <remark> · JATS <statement> · content structured → <children>

attribute	kind	values / default	notes
`name`	kwarg		Optional name suffix for the remark’s label.
`+numbered` / `-numbered`	flag	default off	Whether this remark is numbered.

Produced by: canonical <remark>.

Examples


<remark | The converse does not hold in general.>

Remark.

The converse does not hold in general.

Minipage 101.

<remark>
The hypothesis of compactness is essential here; without it
the conclusion fails (consider $f(x) = 1/x$ on $(0, 1]$).
</remark>

Remark.

The hypothesis of compactness is essential here; without it the conclusion fails (consider $f (x) = 1/ x$ on $(0, 1]$ ).

Minipage 102.

<theorem>

Specification

category theorem-family · eHTML <theorem> · JATS <statement> · content structured → <children>

attribute	kind	values / default	notes
`name`	kwarg		Optional name suffix for the theorem’s label (the “(Pythagoras)” half of “Theorem 1.2 (Pythagoras)”).
`+numbered` / `-numbered`	flag	default on	Whether this theorem participates in the theorem-family shared counter (see “Numbering” below).

Produced by: canonical <theorem>.

Examples


<theorem | If $a^2 + b^2 = c^2$ then the triangle is right-angled.>

Theorem 1.

If $a^{2} + b^{2} = c^{2}$ then the triangle is right-angled.

Minipage 103.

Short-form with pipe content. The body is parsed normally.

<theorem name="Pythagoras" #thm:pyth>
If $a^2 + b^2 = c^2$, the triangle with sides $a$, $b$, $c$
is right-angled.
</theorem>

Theorem 1 (Pythagoras).

If $a^{2} + b^{2} = c^{2}$ , the triangle with sides $a$ , $b$ , $c$ is right-angled.

Minipage 104.

Long-form with the optional name kwarg. Cross-referenceable via id (the “thm:” colon-prefix convention is consistent with “fig:”, “eqn:”, “sec:” elsewhere in enscribe). The name kwarg lifts to data-name; the Phase-2 handler will render it as the “(Pythagoras)” suffix to the label “Theorem N”.