FULL_PROOF preamble: 16 macros, 13 theorem environments, 3 environments; body definitions: ['\\mdsum']

== MAIN (MAIN_RESULT.tex): preamble 6 macros, body definitions []; theorem environments ['corollary', 'definition', 'lemma', 'remark', 'theorem']
  \E             used   {\mathbb{E}}                                                           same
  \Q             unused {\mathbb{Q}}                                                           same
  \R             used   {\mathbb{R}}                                                           same
  \bb            used   {\bar b}                                                               same
  \mb            used   {\bar m}                                                               same
  \ubar          used   {\bar u_0}                                                             same
  theorem env corollary    source \newtheorem{corollary}[theorem]{Corollary}                             FULL_PROOF \newtheorem{corollary}[theorem]{Corollary}
  theorem env definition   source \newtheorem{definition}[theorem]{Definition}                           FULL_PROOF \newtheorem{definition}[theorem]{Definition}
  theorem env lemma        source \newtheorem{lemma}[theorem]{Lemma}                                     FULL_PROOF \newtheorem{lemma}[theorem]{Lemma}
  theorem env remark       source \newtheorem{remark}[theorem]{Remark}                                   FULL_PROOF \newtheorem{remark}[theorem]{Remark}
  theorem env theorem      source \newtheorem{theorem}{Theorem}                                          FULL_PROOF \newtheorem{theorem}{Theorem}[chapter]

== K2 (MAIN_RESULT_K2.tex): preamble 5 macros, body definitions []; theorem environments ['corollary', 'definition', 'lemma', 'remark', 'theorem']
  \E             used   {\mathbb{E}}                                                           same
  \R             used   {\mathbb{R}}                                                           same
  \bb            used   {\bar b}                                                               same
  \mb            used   {\bar m}                                                               same
  \sgn           used   {\operatorname{sgn}}                                                   same
  theorem env corollary    source \newtheorem{corollary}[theorem]{Corollary}                             FULL_PROOF \newtheorem{corollary}[theorem]{Corollary}
  theorem env definition   source \newtheorem{definition}[theorem]{Definition}                           FULL_PROOF \newtheorem{definition}[theorem]{Definition}
  theorem env lemma        source \newtheorem{lemma}[theorem]{Lemma}                                     FULL_PROOF \newtheorem{lemma}[theorem]{Lemma}
  theorem env remark       source \newtheorem{remark}[theorem]{Remark}                                   FULL_PROOF \newtheorem{remark}[theorem]{Remark}
  theorem env theorem      source \newtheorem{theorem}{Theorem}                                          FULL_PROOF \newtheorem{theorem}{Theorem}[chapter]

== K3 (MAIN_RESULT_K3.tex): preamble 5 macros, body definitions []; theorem environments ['corollary', 'definition', 'lemma', 'remark', 'theorem', 'thmthree']
  \E             used   {\mathbb{E}}                                                           same
  \R             used   {\mathbb{R}}                                                           same
  \bb            used   {\bar b}                                                               same
  \mb            used   {\bar m}                                                               same
  \sgn           used   {\operatorname{sgn}}                                                   same
  theorem env corollary    source \newtheorem{corollary}[theorem]{Corollary}                             FULL_PROOF \newtheorem{corollary}[theorem]{Corollary}
  theorem env definition   source \newtheorem{definition}[theorem]{Definition}                           FULL_PROOF \newtheorem{definition}[theorem]{Definition}
  theorem env lemma        source \newtheorem{lemma}[theorem]{Lemma}                                     FULL_PROOF \newtheorem{lemma}[theorem]{Lemma}
  theorem env remark       source \newtheorem{remark}[theorem]{Remark}                                   FULL_PROOF \newtheorem{remark}[theorem]{Remark}
  theorem env theorem      source \newtheorem{theorem}{Theorem}                                          FULL_PROOF \newtheorem{theorem}{Theorem}[chapter]
  theorem env thmthree     source \newtheorem*{thmthree}{Theorem 3}                                      FULL_PROOF \newtheorem*{thmthree}{Theorem 3}

== K3B (MAIN_RESULT_K3B.tex): preamble 6 macros, body definitions []; theorem environments ['corollary', 'definition', 'lemma', 'remark', 'theorem', 'thmfour']
  \E             used   {\mathbb{E}}                                                           same
  \R             used   {\mathbb{R}}                                                           same
  \bb            used   {\bar b}                                                               same
  \cone          unused {\operatorname{cone}}                                                  same
  \mb            used   {\bar m}                                                               same
  \sgn           used   {\operatorname{sgn}}                                                   same
  theorem env corollary    source \newtheorem{corollary}[theorem]{Corollary}                             FULL_PROOF \newtheorem{corollary}[theorem]{Corollary}
  theorem env definition   source \newtheorem{definition}[theorem]{Definition}                           FULL_PROOF \newtheorem{definition}[theorem]{Definition}
  theorem env lemma        source \newtheorem{lemma}[theorem]{Lemma}                                     FULL_PROOF \newtheorem{lemma}[theorem]{Lemma}
  theorem env remark       source \newtheorem{remark}[theorem]{Remark}                                   FULL_PROOF \newtheorem{remark}[theorem]{Remark}
  theorem env theorem      source \newtheorem{theorem}{Theorem}                                          FULL_PROOF \newtheorem{theorem}{Theorem}[chapter]
  theorem env thmfour      source \newtheorem*{thmfour}{Theorem 4}                                       FULL_PROOF \newtheorem*{thmfour}{Theorem 4}

== K4 (MAIN_RESULT_K4.tex): preamble 6 macros, body definitions []; theorem environments ['corollary', 'definition', 'lemma', 'remark', 'theorem', 'thmfive']
  \E             used   {\mathbb{E}}                                                           same
  \R             used   {\mathbb{R}}                                                           same
  \TBD           unused [1]{\textbf{[#1]}}                                                     same
  \bb            used   {\bar b}                                                               same
  \mb            used   {\bar m}                                                               same
  \sgn           used   {\operatorname{sgn}}                                                   same
  theorem env corollary    source \newtheorem{corollary}[theorem]{Corollary}                             FULL_PROOF \newtheorem{corollary}[theorem]{Corollary}
  theorem env definition   source \newtheorem{definition}[theorem]{Definition}                           FULL_PROOF \newtheorem{definition}[theorem]{Definition}
  theorem env lemma        source \newtheorem{lemma}[theorem]{Lemma}                                     FULL_PROOF \newtheorem{lemma}[theorem]{Lemma}
  theorem env remark       source \newtheorem{remark}[theorem]{Remark}                                   FULL_PROOF \newtheorem{remark}[theorem]{Remark}
  theorem env theorem      source \newtheorem{theorem}{Theorem}                                          FULL_PROOF \newtheorem{theorem}{Theorem}[chapter]
  theorem env thmfive      source \newtheorem*{thmfive}{Theorem 5}                                       FULL_PROOF \newtheorem*{thmfive}{Theorem 5}

== K5 (MAIN_RESULT_K5.tex): preamble 6 macros, body definitions []; theorem environments ['corollary', 'definition', 'lemma', 'remark', 'theorem', 'thmsix']
  \E             used   {\mathbb{E}}                                                           same
  \R             used   {\mathbb{R}}                                                           same
  \TBD           unused [1]{\textbf{[#1]}}                                                     same
  \bb            used   {\bar b}                                                               same
  \mb            used   {\bar m}                                                               same
  \sgn           used   {\operatorname{sgn}}                                                   same
  theorem env corollary    source \newtheorem{corollary}[theorem]{Corollary}                             FULL_PROOF \newtheorem{corollary}[theorem]{Corollary}
  theorem env definition   source \newtheorem{definition}[theorem]{Definition}                           FULL_PROOF \newtheorem{definition}[theorem]{Definition}
  theorem env lemma        source \newtheorem{lemma}[theorem]{Lemma}                                     FULL_PROOF \newtheorem{lemma}[theorem]{Lemma}
  theorem env remark       source \newtheorem{remark}[theorem]{Remark}                                   FULL_PROOF \newtheorem{remark}[theorem]{Remark}
  theorem env theorem      source \newtheorem{theorem}{Theorem}                                          FULL_PROOF \newtheorem{theorem}{Theorem}[chapter]
  theorem env thmsix       source \newtheorem*{thmsix}{Theorem 6}                                        FULL_PROOF \newtheorem*{thmsix}{Theorem 6}

== RQB (RQB_MAIN_RESULT.tex): preamble 5 macros, body definitions []; theorem environments ['conjecture', 'corollary', 'definition', 'lemma', 'proposition', 'remark', 'theorem']
  \E             used   {\mathbb{E}}                                                           same
  \N             used   {\mathbb{N}}                                                           same
  \R             used   {\mathbb{R}}                                                           same
  \Rid           used   {R_{\mathrm{ID}}}                                                      same
  \sgn           used   {\operatorname{sgn}}                                                   same
  theorem env conjecture   source \newtheorem{conjecture}[theorem]{Conjecture}                           FULL_PROOF \newtheorem{conjecture}[theorem]{Conjecture}
  theorem env corollary    source \newtheorem{corollary}[theorem]{Corollary}                             FULL_PROOF \newtheorem{corollary}[theorem]{Corollary}
  theorem env definition   source \newtheorem{definition}[theorem]{Definition}                           FULL_PROOF \newtheorem{definition}[theorem]{Definition}
  theorem env lemma        source \newtheorem{lemma}[theorem]{Lemma}                                     FULL_PROOF \newtheorem{lemma}[theorem]{Lemma}
  theorem env proposition  source \newtheorem{proposition}[theorem]{Proposition}                         FULL_PROOF \newtheorem{proposition}[theorem]{Proposition}
  theorem env remark       source \newtheorem{remark}[theorem]{Remark}                                   FULL_PROOF \newtheorem{remark}[theorem]{Remark}
  theorem env theorem      source \newtheorem{theorem}{Theorem}[section]                                 FULL_PROOF \newtheorem{theorem}{Theorem}[chapter]

== RQD (RQD_MAIN_RESULT.tex): preamble 4 macros, body definitions []; theorem environments ['corollary', 'definition', 'lemma', 'proposition', 'remark', 'theorem']
  \E             used   {\mathbb{E}}                                                           same
  \PP            used   {\mathbb{P}}                                                           same
  \R             used   {\mathbb{R}}                                                           same
  \sgn           used   {\operatorname{sgn}}                                                   same
  theorem env corollary    source \newtheorem{corollary}[theorem]{Corollary}                             FULL_PROOF \newtheorem{corollary}[theorem]{Corollary}
  theorem env definition   source \newtheorem{definition}[theorem]{Definition}                           FULL_PROOF \newtheorem{definition}[theorem]{Definition}
  theorem env lemma        source \newtheorem{lemma}[theorem]{Lemma}                                     FULL_PROOF \newtheorem{lemma}[theorem]{Lemma}
  theorem env proposition  source \newtheorem{proposition}[theorem]{Proposition}                         FULL_PROOF \newtheorem{proposition}[theorem]{Proposition}
  theorem env remark       source \newtheorem{remark}[theorem]{Remark}                                   FULL_PROOF \newtheorem{remark}[theorem]{Remark}
  theorem env theorem      source \newtheorem{theorem}{Theorem}                                          FULL_PROOF \newtheorem{theorem}{Theorem}[chapter]

== macros defined by more than one source with different bodies

used macros whose definition is missing or different in FULL_PROOF: 0
A41G_PASS
