theorem

A callout stating a formal result, with its proof held back in the detail.

theoremNode
On this page

#Attributes

kindImplicit
What the result is, and the word that heads it: theorem, lemma, proposition, corollary, conjecture or claim. It fills the head's slot, so theorem:lemma{…} is the usual spelling.
theoremlemmapropositioncorollaryconjectureclaim
Can be written as shorthand: theorem:value
Defaulttheorem
title
The result's name, set after the label: Mean value theorem. Rich text, so $…$ maths and inline formatting set in it. Without one, the label stands alone.
rich-text

#Allowed content

Body { }
paragraphh1h2h3h4listequation
Detail [ ]
paragraphh1h2h3h4listequation

#Allowed in

scene { }

#Examples

theorem{
    If $f$ is continuous on $[a, b]$ and differentiable on $(a, b)$, some $c$ in $(a, b)$ has $f'(c) = \frac{f(b) - f(a)}{b - a}$.
}(
    title: Mean value theorem
)
theorem:lemma{
    For integers $a$ and $b$, not both zero, there are integers $x$ and $y$ with $ax + by = \gcd(a, b)$.
}[
    The set $\{ax + by > 0\}$ is non-empty, so it has a least element $d$. Dividing $a$ by $d$ leaves a remainder in the set smaller than $d$, so the remainder is 0 and $d$ divides $a$; likewise $b$. Any common divisor of $a$ and $b$ divides $d$, so $d = \gcd(a, b)$.
](
    title: Bézout's identity
)
theorem:conjecture{
    Every even integer greater than 2 is the sum of two primes.
}(
    title: Goldbach
)

#Notes

  • It is headed by its kind and its number, then the title; the body is the statement.
  • The optional detail is the proof, folded under a Proof button. It starts folded every time the page loads.
  • Every kind counts on one number through the internote, so a lemma written after a theorem is LEMMA 2. Definitions, notes and the other callouts keep counts of their own.
  • Of the callouts, a task and a theorem take a detail.
  • Narrative only: a callout in a scene's detail is refused.
  • Callouts do not nest, and none takes a divider or an internote card in its body.
  • Narration reads the label, the title and the statement. It does not read the proof.

#Writing guidance

  • Callouts — Prose around every callout, one job each, a definition written to stand in a glossary, and which callout a result, a hazard or a set-apart panel takes.

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