@Section
   @Title { Theorems, lemmas, corollaries, definitions, propositions,
examples, and claims }
   @RunningTitle { Theorems, lemmas, etc. }
   @Tag { theorems }
@Begin
@PP
theorem. @Index @Code "@Theorem"
A theorem is created like this:
@ID @Code {
"@LD @Theorem"
"    @Title { Fermat's Last Theorem }"
"{"
"@Eq { a sup n + b sup n != c sup n } for all positive"
"integers @Eq { a }, @Eq { b }, @Eq { c } and @Eq { n }"
"when @Eq { n > 2 }."
"@LP"
"@Proof I have a proof of this theorem, but the margin"
"is too small to contain it. @EndProof"
"}"
}
where we have used the @Code "@LD" `left display' symbol from
Section {@NumberOf displays} to get a left-justified display,
and the @Code "@Eq" symbol from Chapter {@NumberOf equations}
for the equations.  The result is
@ID @Theorem
    @Title { Fermat's Last Theorem }
{
@Eq { a sup n + b sup n != c sup n } for all positive
integers @Eq { a }, @Eq { b }, @Eq { c } and @Eq { n }
when @Eq { n > 2 }.
@LP
@Proof I have a proof of this theorem, but the margin
is too small to contain it. @EndProof
}
The @Code "@Theorem" symbol produces an object with no adjacent
vertical space, hence it needs to be used in conjuction with
display or paragraph symbols.  The theorem is numbered automatically,
with the title and number inserted at the start of the first
paragraph.  @Code "@Title" may be omitted.
@PP
The @Code "@Proof" symbol produces @Proof @Null
proof. @Index @Code "@Proof"
with the appropriate following space, and the @Code "@EndProof" symbol produces
endproof. @Index @Code "@EndProof"
a box at the end of the line.  They may be used anywhere, not
just within theorems.
@PP
There are seven symbols that produce independently numbered sequences
in this way.  They are {@Code "@Theorem"}, {@Code "@Definition"},
definition. @Index @Code "@Definition"
claim. @Index @Code "@Claim"
proposition. @Index @Code "@Proposition"
lemma. @Index @Code "@Lemma"
corollary. @Index @Code "@Corollary"
example. @Index @Code "@Example"
{@Code "@Claim"}, {@Code "@Proposition"}, {@Code "@Lemma"},
{@Code "@Corollary"}, and {@Code "@Example"}.
@PP
The setup file contains options which determine whether the theorem
numbers include a chapter number ({@Code "@ChapterNumInTheorems"}),
or a section number ({@Code "@SectionNumInTheorems"}), and so on.  A
section number automatically includes a chapter number, etc.  There
are also options to change the word printed.  For example, if you
need a sequence of conjectures, change the @Code "@ClaimWord" setup
file option to
@ID @Code "@ClaimWord { Conjecture }"
and use the @Code "@Claim" symbol for your conjectures.  You can even put
@ID @Code {
"import @DocumentLayout"
"macro @Conjecture { @Claim }"
}
into your @Code mydefs file (Section {@NumberOf definitions}) if you wish,
so that you can write @Code "@Conjecture" in your documents instead of
{@Code "@Claim"}.
@PP
Owing to problems behind the scenes, the @Code "@Theorem" symbol and its
companions have a potential efficiency problem:  although all numbers are
finalized on the second run, it takes Lout time proportional to the square
of the highest theorem number to do this.  So large numbers of theorems
numbered together might be slow.
@End @Section
