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authoradelon <22380201+adelon@users.noreply.github.com>2025-08-12 00:37:28 +0200
committeradelon <22380201+adelon@users.noreply.github.com>2025-08-12 00:37:28 +0200
commit39ef87d3ce39152febc130aa95e25dc0722c3525 (patch)
tree018ce21f85bc132306ac5130db405527a313c1a7 /library/topology/urysohntwo.tex
parentafce89ead823b6e9eec4a0b115bbe57a89a8e912 (diff)
Allow relation symbols with parameters
Parameters must follow the relation symbol and be surrounded by braces, like so: `\rel{x}{y}{z}`. This attempt is still brittle/broken in a few ways: - It makes using braces in creative ways in mixfix notation ambiguous. - It does not verify that the parameters are used in a consistent manner for each symbol. It essentially allows users to define `a\MyRel b` and `a\MyRel{x} b` (and ones with even more parameters). - It allows parameters for all relation symbols, even for those where it makes no sense in ordinary TeX markup, e.g. `a <{x} b`.
Diffstat (limited to 'library/topology/urysohntwo.tex')
-rw-r--r--library/topology/urysohntwo.tex2
1 files changed, 1 insertions, 1 deletions
diff --git a/library/topology/urysohntwo.tex b/library/topology/urysohntwo.tex
index eda3c32..7f69aa4 100644
--- a/library/topology/urysohntwo.tex
+++ b/library/topology/urysohntwo.tex
@@ -473,7 +473,7 @@
\begin{proof}[Proof by \in-induction on $n$]
Assume $n \in \naturals$.
Suppose $Y$ has cardinality $n$.
- $X$ has cardinality $n$ by \cref{bijection_converse_is_bijection,bijection_circ,regularity,cardinality,foundation,empty_eq,emptyset}.
+ $X$ has cardinality $n$ by \cref{bijection_converse_is_bijection,bijection_circ,regularity,cardinality,foundation,emptyset}.
\begin{byCase}
\caseOf{$n = \zero$.}
Follows by \cref{converse_converse_eq,injective_converse_is_function,converse_is_relation,dom_converse,id_is_function_to,id_ran,ran_circ_exact,circ,ran_converse,emptyset_is_function_on_emptyset,bijective_converse_are_funs,relext,function_member_elim,bijection_is_function,cardinality,bijections_dom,in_irrefl,codom_of_emptyset_can_be_anything,converse_emptyset,funs_elim,neq_witness,id}.