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/usr/share/lyx/layouts/theorems-ams-extended.module is in lyx-common 2.2.2-1.

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#\DeclareLyXModule{Theorems (AMS-Extended)}
#DescriptionBegin
#Defines some additional theorem environments for use with the
#AMS theorems packages. Includes Criterion, Algorithm, Axiom,
#Condition, Note, Notation, Summary, Acknowledgement, Conclusion,
#Fact, Assumption, Case, and Question, in both numbered and non-numbered
#forms.
#DescriptionEnd
#Requires: theorems-ams
#Category: theorems

# Original Author : David L. Johnson <dlj0@lehigh.edu>
# Probably broken by Jean-Marc Lasgouttes <Jean-Marc.Lasgouttes@inria.fr>
# modified and modularized by Emmanuel GUREGHIAN <gureghia@boston.bertin.fr>
# Tinkered with Sep. '07 by Paul Rubin <rubin@msu.edu>
# Modularized Jan 08 by Richard Heck <rgheck@comcast.net>

Format 60

Requires	amsmath

# The environments defined (regular and starred) are :
# - Criterion
# - Algorithm
# - Axiom
# - Condition
# - Note
# - Notation
# - Summary
# - Acknowledgement
# - Conclusion
# - Fact
# - Assumption
# - Question

Style Criterion
	CopyStyle             Theorem
	DependsOn	            Theorem
	LatexName             criterion
	LabelString           "Criterion \thetheorem."
	Preamble
	  \theoremstyle{plain}
	  \newtheorem{criterion}[thm]{\protect\criterionname}
	EndPreamble
	LangPreamble
	  \providecommand{\criterionname}{_(Criterion)}
	EndLangPreamble
	BabelPreamble
	  \addto\captions$$lang{\renewcommand{\criterionname}{_(Criterion)}}
	EndBabelPreamble
End

Style Criterion*
	CopyStyle             Theorem*
	LatexName             criterion*
	LabelString           "Criterion."
	Preamble
	  \theoremstyle{plain}
	  \newtheorem*{criterion*}{\protect\criterionname}
	EndPreamble
	LangPreamble
	  \providecommand{\criterionname}{_(Criterion)}
	EndLangPreamble
	BabelPreamble
	  \addto\captions$$lang{\renewcommand{\criterionname}{_(Criterion)}}
	EndBabelPreamble
End


Style Algorithm
	CopyStyle             Theorem
	DependsOn	           Theorem
	LatexName             lyxalgorithm
	LabelString           "Algorithm \thetheorem."
	Preamble
	  \theoremstyle{plain}
	  \newtheorem{lyxalgorithm}[thm]{\protect\algorithmname}
	EndPreamble
	LangPreamble
	  \providecommand{\algorithmname}{_(Algorithm)}
	EndLangPreamble
	BabelPreamble
	  \addto\captions$$lang{\renewcommand{\algorithmname}{_(Algorithm)}}
	EndBabelPreamble
End


Style Algorithm*
	CopyStyle             Theorem*
	LatexName             lyxalgorithm*
	LabelString           "Algorithm."
	Preamble
	  \theoremstyle{plain}
	  \newtheorem*{lyxalgorithm*}{\protect\algorithmname}
	EndPreamble
	LangPreamble
	  \providecommand{\algorithmname}{_(Algorithm)}
	EndLangPreamble
	BabelPreamble
	  \addto\captions$$lang{\renewcommand{\algorithmname}{_(Algorithm)}}
	EndBabelPreamble
End


Style Axiom
	CopyStyle             Theorem
	DependsOn	            Theorem
	LatexName             ax
	LabelString           "Axiom \thetheorem."
	Preamble
	  \theoremstyle{plain}
	  \newtheorem{ax}[thm]{\protect\axiomname}
	EndPreamble
	LangPreamble
	  \providecommand{\axiomname}{_(Axiom)}
	EndLangPreamble
	BabelPreamble
	  \addto\captions$$lang{\renewcommand{\axiomname}{_(Axiom)}}
	EndBabelPreamble
End


Style Axiom*
	CopyStyle             Theorem*
	LatexName             ax*
	LabelString           "Axiom."
	Preamble
	  \theoremstyle{plain}
	  \newtheorem*{ax*}{\protect\axiomname}
	EndPreamble
	LangPreamble
	  \providecommand{\axiomname}{_(Axiom)}
	EndLangPreamble
	BabelPreamble
	  \addto\captions$$lang{\renewcommand{\axiomname}{_(Axiom)}}
	EndBabelPreamble
End


Style Condition
	CopyStyle             Definition
	LatexName             condition
	LabelString           "Condition \thetheorem."
	Preamble
	  \theoremstyle{definition}
	  \newtheorem{condition}[thm]{\protect\conditionname}
	EndPreamble
	LangPreamble
	  \providecommand{\conditionname}{_(Condition)}
	EndLangPreamble
	BabelPreamble
	  \addto\captions$$lang{\renewcommand{\conditionname}{_(Condition)}}
	EndBabelPreamble
End


Style Condition*
	CopyStyle             Definition*
	LatexName             condition*
	LabelString           "Condition."
	Preamble
	  \theoremstyle{definition}
	  \newtheorem*{condition*}{\protect\conditionname}
	EndPreamble
	LangPreamble
	  \providecommand{\conditionname}{_(Condition)}
	EndLangPreamble
	BabelPreamble
	  \addto\captions$$lang{\renewcommand{\conditionname}{_(Condition)}}
	EndBabelPreamble
End


Style Note
	CopyStyle             Remark
	LatexName             note
	LabelString           "Note \thetheorem."
	Preamble
	  \theoremstyle{remark}
	  \newtheorem{note}[thm]{\protect\notename}
	EndPreamble
	LangPreamble
	  \providecommand{\notename}{_(Note)}
	EndLangPreamble
	BabelPreamble
	  \addto\captions$$lang{\renewcommand{\notename}{_(Note)}}
	EndBabelPreamble
End


Style Note*
	CopyStyle             Remark*
	LatexName             note*
	LabelString           "Note."
	Preamble
	  \theoremstyle{remark}
	  \newtheorem*{note*}{\protect\notename}
	EndPreamble
	LangPreamble
	  \providecommand{\notename}{_(Note)}
	EndLangPreamble
	BabelPreamble
	  \addto\captions$$lang{\renewcommand{\notename}{_(Note)}}
	EndBabelPreamble
End


Style Notation
	CopyStyle             Remark
	LatexName             notation
	LabelString           "Notation \thetheorem."
	Preamble
	  \theoremstyle{remark}
	  \newtheorem{notation}[thm]{\protect\notationname}
	EndPreamble
	LangPreamble
	  \providecommand{\notationname}{_(Notation)}
	EndLangPreamble
	BabelPreamble
	  \addto\captions$$lang{\renewcommand{\notationname}{_(Notation)}}
	EndBabelPreamble
End


Style Notation*
	CopyStyle             Remark*
	LatexName             notation*
	LabelString           "Notation."
	Preamble
	  \theoremstyle{remark}
	  \newtheorem*{notation*}{\protect\notationname}
	EndPreamble
	LangPreamble
	  \providecommand{\notationname}{_(Notation)}
	EndLangPreamble
	BabelPreamble
	  \addto\captions$$lang{\renewcommand{\notationname}{_(Notation)}}
	EndBabelPreamble
End


Style Summary
	CopyStyle             Remark
	LatexName             summary
	LabelString           "Summary \thetheorem."
	Preamble
	  \theoremstyle{remark}
	  \newtheorem{summary}[thm]{\protect\summaryname}
	EndPreamble
	LangPreamble
	  \providecommand{\summaryname}{_(Summary)}
	EndLangPreamble
	BabelPreamble
	  \addto\captions$$lang{\renewcommand{\summaryname}{_(Summary)}}
	EndBabelPreamble
End


Style Summary*
	CopyStyle             Remark*
	LatexName             summary*
	LabelString           "Summary."
	Preamble
	  \theoremstyle{remark}
	  \newtheorem*{summary*}{\protect\summaryname}
	EndPreamble
	LangPreamble
	  \providecommand{\summaryname}{_(Summary)}
	EndLangPreamble
	BabelPreamble
	  \addto\captions$$lang{\renewcommand{\summaryname}{_(Summary)}}
	EndBabelPreamble
End


Style Acknowledgement
	CopyStyle             Remark
	LatexName             acknowledgement
	LabelString           "Acknowledgement \thetheorem."
	Preamble
	  \theoremstyle{remark}
	  \newtheorem{acknowledgement}[thm]{\protect\acknowledgementname}
	EndPreamble
	LangPreamble
	  \providecommand{\acknowledgementname}{_(Acknowledgement)}
	EndLangPreamble
	BabelPreamble
	  \addto\captions$$lang{\renewcommand{\acknowledgementname}{_(Acknowledgement)}}
	EndBabelPreamble
End


Style Acknowledgement*
	CopyStyle             Remark*
	LatexName             acknowledgement*
	LabelString           "Acknowledgement."
	Preamble
	  \theoremstyle{remark}
	  \newtheorem*{acknowledgement*}{\protect\acknowledgementname}
	EndPreamble
	LangPreamble
	  \providecommand{\acknowledgementname}{_(Acknowledgement)}
	EndLangPreamble
	BabelPreamble
	  \addto\captions$$lang{\renewcommand{\acknowledgementname}{_(Acknowledgement)}}
	EndBabelPreamble
End


Style Conclusion
	CopyStyle             Remark
	LatexName             conclusion
	LabelString           "Conclusion \thetheorem."
	Preamble
	  \theoremstyle{remark}
	  \newtheorem{conclusion}[thm]{\protect\conclusionname}
	EndPreamble
	LangPreamble
	  \providecommand{\conclusionname}{_(Conclusion)}
	EndLangPreamble
	BabelPreamble
	  \addto\captions$$lang{\renewcommand{\conclusionname}{_(Conclusion)}}
	EndBabelPreamble
End


Style Conclusion*
	CopyStyle             Remark*
	LatexName             conclusion*
	LabelString           "Conclusion."
	Preamble
	  \theoremstyle{remark}
	  \newtheorem*{conclusion*}{\protect\conclusionname}
	EndPreamble
	LangPreamble
	  \providecommand{\conclusionname}{_(Conclusion)}
	EndLangPreamble
	BabelPreamble
	  \addto\captions$$lang{\renewcommand{\conclusionname}{_(Conclusion)}}
	EndBabelPreamble
End


Style Assumption
	CopyStyle             Theorem
	DependsOn	            Theorem
	LatexName             assumption
	LabelString           "Assumption \thetheorem."
	Preamble
	  \theoremstyle{plain}
	  \newtheorem{assumption}[thm]{\protect\assumptionname}
	EndPreamble
	LangPreamble
	  \providecommand{\assumptionname}{_(Assumption)}
	EndLangPreamble
	BabelPreamble
	  \addto\captions$$lang{\renewcommand{\assumptionname}{_(Assumption)}}
	EndBabelPreamble
End


Style Assumption*
	CopyStyle             Theorem*
	LatexName             assumption*
	LabelString           "Assumption."
	Preamble
	  \theoremstyle{plain}
	  \newtheorem*{assumption*}{\protect\assumptionname}
	EndPreamble
	LangPreamble
	  \providecommand{\assumptionname}{_(Assumption)}
	EndLangPreamble
	BabelPreamble
	  \addto\captions$$lang{\renewcommand{\assumptionname}{_(Assumption)}}
	EndBabelPreamble
End

Style Question
	CopyStyle             Theorem
	DependsOn             Theorem
	LatexName             question
	LabelString           "Question \thetheorem."
	Preamble
	  \theoremstyle{plain}
	  \newtheorem{question}[thm]{\protect\questionname}
	EndPreamble
	LangPreamble
	  \providecommand{\questionname}{_(Question)}
	EndLangPreamble
	BabelPreamble
	  \addto\captions$$lang{\renewcommand{\questionname}{_(Question)}}
	EndBabelPreamble
End

Style Question*
	CopyStyle             Theorem*
	LatexName             question*
	LabelString           "Question."
	Preamble
	  \theoremstyle{plain}
	  \newtheorem*{question*}{\protect\questionname}
	EndPreamble
	LangPreamble
	  \providecommand{\questionname}{_(Question)}
	EndLangPreamble
	BabelPreamble
	  \addto\captions$$lang{\renewcommand{\questionname}{_(Question)}}
	EndBabelPreamble
End

Input theorems-refprefix.inc