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rendering fixes
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SKolodynski committed May 31, 2024
1 parent 870c41a commit 6c39dd9
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4 changes: 2 additions & 2 deletions IsarMathLib/MetricSpace_ZF_1.thy
Original file line number Diff line number Diff line change
Expand Up @@ -44,8 +44,8 @@ text\<open> The \<open>reals\<close> context (locale) defined in the \<open>Real
positive numbers, absolute value etc. For metric spaces we reuse the notation defined there.\<close>

text\<open>The \<open>pmetric_space1\<close> locale extends the \<open>reals\<close> locale, adding the carrier $X$
of the metric space and the metric $\mathfrak{d}$ to the context, together with the assumption
that $\mathfrak{d}:X\times X \rightarrow \mathbb{R}$ is a pseudo metric.
of the metric space and the metric $\mathcal{d}$ to the context, together with the assumption
that $\mathcal{d}:X\times X \rightarrow \mathbb{R}^+$ is a pseudo metric.
An alternative would be to define the \<open>pmetric_space1\<close> as an extension of the \<open>pmetric_space1\<close>
context, but that is in turn an extension of the \<open>loop1\<close> locale that defines notation
for left and right division which which do not want in the context of real numbers. \<close>
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14 changes: 6 additions & 8 deletions IsarMathLib/Topology_ZF_examples.thy
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Expand Up @@ -224,19 +224,17 @@ proof-
ultimately show ?thesis by auto
qed

text\<open> $X$ is a closed set that contains $A$.
This lemma is necessary because we cannot
use the lemmas proven in the \<open>topology0\<close> context since
\<open> T\<noteq>0"} \<close> is too weak for
\<open>CoCardinal(X,T)\<close> to be a topology.\<close>
text\<open> $X$ is a closed set that contains $A$.
This lemma is necessary because we cannot use the lemmas proven in the
\<open>topology0\<close> context since $T\<noteq>0$ is too weak for \<open>CoCardinal(X,T)\<close>
to be a topology.\<close>

lemma X_closedcov_cocardinal:
assumes "T\<noteq>0" "A\<subseteq>X"
shows "X\<in>ClosedCovers(A,CoCardinal(X,T))" using ClosedCovers_def
shows "X \<in> ClosedCovers(A,CoCardinal(X,T))" using ClosedCovers_def
using union_cocardinal closed_sets_cocardinal assms by auto

text\<open>The closure of a set is itself if it is closed or \<open>X\<close> if
it isn't closed.\<close>
text\<open>The closure of a set is itself if it is closed or $X$ if it isn't closed.\<close>

lemma closure_set_cocardinal:
assumes "T\<noteq>0""A\<subseteq>X"
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1 change: 1 addition & 0 deletions isar2html2.0/src/isar2html/IsarSym2Latex.fs
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Expand Up @@ -123,6 +123,7 @@ namespace iml
("\\<S>", "\\mathcal{S} ")
("\\<T>", "\\mathcal{T} ")
("\\<X>", "\\mathcal{X} ")
("\\<d>", "\\mathcal{d} ")
("\\<ra>", " + ")
("\\<rd>", "/ ")
("\\<rm>", " - ")
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