\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{thm\_2Ebinary\_\_ieee\_2Efloat\_\_literal\_\_11 (TMSzWy2rDH6EF5Aiv5W3xMUmd8QBAozMvi7)}
\maketitle
Let $ c\_2Ebool\_2EARB : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} A\_27a .  {{{nonempty}~{A\_27a}}{\unicdbdjdcd}{{{c\_2Ebool\_2EARB}~{A\_27a}} \in {A\_27a}}}}\label{hyp:ngfgngpfdgpfcdfecgpgpgmgpfcdfebecfce}
\end{equation}
Let $ ty\_2Ebinary\_\_ieee\_2Efloat : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} A0 .  nonempty~A0{\unicdbdjdcd}{\unicdcdadad} A1 .  nonempty~A1{\unicdbdjdcd}nonempty~(ty\_2Ebinary\_\_ieee\_2Efloat~\\
A0~A1)\end{array}
\label{hyp:ogfgpfehjhpfcdfecgjgogbgchjhpfpfjgfgfgfgpfcdfeggmgpgbgeh}
\end{equation}
Let $ ty\_2Eone\_2Eone : {\iota}$ be given.
Assume the following.
\begin{equation}
{{nonempty}~{ty\_2Eone\_2Eone}}\label{hyp:ogfgpfehjhpfcdfepgogfgpfcdfepgogfg}
\end{equation}
Let $ ty\_2Efcp\_2Ecart : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} A0 .  nonempty~A0{\unicdbdjdcd}{\unicdcdadad} A1 .  nonempty~A1{\unicdbdjdcd}nonempty~(ty\_2Efcp\_2Ecart~\\
A0~A1)\end{array}
\label{hyp:ogfgpfehjhpfcdfeggdgahpfcdfedgbgcheh}
\end{equation}
Let $ c\_2Ebinary\_\_ieee\_2Efloat\_\_Sign\_\_fupd : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} A\_27t .  nonempty~A\_27t{\unicdbdjdcd}{\unicdcdadad} A\_27w .  nonempty~A\_27w{\unicdbdjdcd}c\_2Ebinary\_\_ieee\_2Efloat\_\_Sign\_\_fupd~\\
A\_27t~A\_27w \in (((ty\_2Ebinary\_\_ieee\_2Efloat~A\_27t~A\_27w)^{{({{{ty\_2Ebinary\_\_ieee\_2Efloat}~{A\_27t}}~{A\_27w}})}})^{{({{({{{ty\_2Efcp\_2Ecart}~{2}}~{ty\_2Eone\_2Eone}})}^{{({{{ty\_2Efcp\_2Ecart}~{2}}~{ty\_2Eone\_2Eone}})}}})}})\end{array}
\label{hyp:ngfgngpfdgpfcdfecgjgogbgchjhpfpfjgfgfgfgpfcdfeggmgpgbgehpfpfdfjghgogpfpfggfhaheg}
\end{equation}
Let $ c\_2Ebinary\_\_ieee\_2Efloat\_\_Significand\_\_fupd : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} A\_27t .  nonempty~A\_27t{\unicdbdjdcd}{\unicdcdadad} A\_27u .  nonempty~A\_27u{\unicdbdjdcd}{\unicdcdadad} A\_27w .  \\
nonempty~A\_27w{\unicdbdjdcd}c\_2Ebinary\_\_ieee\_2Efloat\_\_Significand\_\_fupd~\\
A\_27t~A\_27u~A\_27w \in (((ty\_2Ebinary\_\_ieee\_2Efloat~A\_27u~A\_27w)^{{({{{ty\_2Ebinary\_\_ieee\_2Efloat}~{A\_27t}}~{A\_27w}})}})^{{({{({{{ty\_2Efcp\_2Ecart}~{2}}~{A\_27u}})}^{{({{{ty\_2Efcp\_2Ecart}~{2}}~{A\_27t}})}}})}})\end{array}
\label{hyp:ngfgngpfdgpfcdfecgjgogbgchjhpfpfjgfgfgfgpfcdfeggmgpgbgehpfpfdfjghgogjgggjgdgbgogegpfpfggfhaheg}
\end{equation}
Let $ c\_2Ebinary\_\_ieee\_2Efloat\_\_Exponent\_\_fupd : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} A\_27t .  nonempty~A\_27t{\unicdbdjdcd}{\unicdcdadad} A\_27w .  nonempty~A\_27w{\unicdbdjdcd}{\unicdcdadad} A\_27x .  \\
nonempty~A\_27x{\unicdbdjdcd}c\_2Ebinary\_\_ieee\_2Efloat\_\_Exponent\_\_fupd~A\_27t~\\
A\_27w~A\_27x \in (((ty\_2Ebinary\_\_ieee\_2Efloat~A\_27t~A\_27x)^{{({{{ty\_2Ebinary\_\_ieee\_2Efloat}~{A\_27t}}~{A\_27w}})}})^{{({{({{{ty\_2Efcp\_2Ecart}~{2}}~{A\_27x}})}^{{({{{ty\_2Efcp\_2Ecart}~{2}}~{A\_27w}})}}})}})\end{array}
\label{hyp:ngfgngpfdgpfcdfecgjgogbgchjhpfpfjgfgfgfgpfcdfeggmgpgbgehpfpffeihahpgogfgogehpfpfggfhaheg}
\end{equation}
Let $ c\_2Ebinary\_\_ieee\_2Efloat\_\_Significand : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} A\_27t .  nonempty~A\_27t{\unicdbdjdcd}{\unicdcdadad} A\_27w .  nonempty~A\_27w{\unicdbdjdcd}c\_2Ebinary\_\_ieee\_2Efloat\_\_Significand~\\
A\_27t~A\_27w \in ((ty\_2Efcp\_2Ecart~2~A\_27t)^{{({{{ty\_2Ebinary\_\_ieee\_2Efloat}~{A\_27t}}~{A\_27w}})}})\end{array}
\label{hyp:ngfgngpfdgpfcdfecgjgogbgchjhpfpfjgfgfgfgpfcdfeggmgpgbgehpfpfdfjghgogjgggjgdgbgogeg}
\end{equation}
Let $ c\_2Ebinary\_\_ieee\_2Efloat\_\_Exponent : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} A\_27t .  nonempty~A\_27t{\unicdbdjdcd}{\unicdcdadad} A\_27w .  nonempty~A\_27w{\unicdbdjdcd}c\_2Ebinary\_\_ieee\_2Efloat\_\_Exponent~\\
A\_27t~A\_27w \in ((ty\_2Efcp\_2Ecart~2~A\_27w)^{{({{{ty\_2Ebinary\_\_ieee\_2Efloat}~{A\_27t}}~{A\_27w}})}})\end{array}
\label{hyp:ngfgngpfdgpfcdfecgjgogbgchjhpfpfjgfgfgfgpfcdfeggmgpgbgehpfpffeihahpgogfgogeh}
\end{equation}
Let $ c\_2Ebinary\_\_ieee\_2Efloat\_\_Sign : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} A\_27t .  nonempty~A\_27t{\unicdbdjdcd}{\unicdcdadad} A\_27w .  nonempty~A\_27w{\unicdbdjdcd}c\_2Ebinary\_\_ieee\_2Efloat\_\_Sign~\\
A\_27t~A\_27w \in ((ty\_2Efcp\_2Ecart~2~ty\_2Eone\_2Eone)^{{({{{ty\_2Ebinary\_\_ieee\_2Efloat}~{A\_27t}}~{A\_27w}})}})\end{array}
\label{hyp:ngfgngpfdgpfcdfecgjgogbgchjhpfpfjgfgfgfgpfcdfeggmgpgbgehpfpfdfjghgog}
\end{equation}
\begin{definition}\label{def:dgpfcdfengjgogpfcdfepfddeepfddeepfddfe}
We define $\mname{c\_2Emin\_2E\_3D\_3D\_3E}$ to be ${{\uniddcgcg} P \in {2} .  {{\uniddcgcg} Q \in {2} .  {{inj\_\_o}~{({{{p}~{P}}{\unicdbdjdcd}{{p}~{Q}}})}}}}$ of type ${\iota}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfengjgogpfcdfepfddee}
We define $\mname{c\_2Emin\_2E\_3D}$ to be ${{\uniddcgcg} A .  {{\uniddcgcg} x \in {A} .  {{\uniddcgcg} y \in {A} .  {{inj\_\_o}~{({{x}={y}})}}}}}$ of type ${{\iota}{\unicdbdjdcd}{\iota}}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfecgpgpgmgpfcdfeef}
We define $\mname{c\_2Ebool\_2ET}$ to be ${({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{({{2}^{{2}}})}})}}~{({{\uniddcgcg} V0x \in {2} .  {V0x}})}})}}~{({{\uniddcgcg} V1x \in {2} .  {V1x}})}})}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfecgpgpgmgpfcdfepfcdbd}
We define $\mname{c\_2Ebool\_2E\_21}$ to be ${{\uniddcgcg} A\_27a : {\iota} .  {({{\uniddcgcg} V0P \in {({{2}^{{A\_27a}}})} .  {({{{ap}~{({{{ap}~{({{\mname{c\_2Emin\_2E\_3D}}~{({{2}^{{A\_27a}}})}})}}~{V0P}})}}~{({{\uniddcgcg} V1x \in {A\_27a} .  {\mname{c\_2Ebool\_2ET}}})}})}})}}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfecgpgpgmgpfcdfepfcdgepffdde}
We define $\mname{c\_2Ebool\_2E\_2F\_5C}$ to be ${({{\uniddcgcg} V0t1 \in {2} .  {({{\uniddcgcg} V1t2 \in {2} .  {({{{ap}~{({{\mname{c\_2Ebool\_2E\_21}}~{2}})}}~{({{\uniddcgcg} V2t \in {2} .  {({{{ap}~{({{{ap}~{\mname{c\_2Emin\_2E\_3D\_3D\_3E}}}~{({{{ap}~{({{{ap}~{\mname{c\_2Emin\_2E\_3D\_3D\_3E}}}~{V0t1}})}}~{({{{ap}~{({{{ap}~{\mname{c\_2Emin\_2E\_3D\_3D\_3E}}}~{V1t2}})}}~{V2t}})}})}})}}~{V2t}})}})}})}})}})}$.
\end{definition}
\begin{definition}\label{def:dgpfcdfedgpgngcgjgogpfcdfele}
We define $\mname{c\_2Ecombin\_2EK}$ to be ${{\uniddcgcg} A\_27a : {\iota} .  {{\uniddcgcg} A\_27b : {\iota} .  {({{\uniddcgcg} V0x \in {A\_27a} .  {({{\uniddcgcg} V1y \in {A\_27b} .  {V0x}})}})}}}$.
\end{definition}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} A\_27t .  nonempty~A\_27t{\unicdbdjdcd}{\unicdcdadad} A\_27u .  nonempty~A\_27u{\unicdbdjdcd}{\unicdcdadad} A\_27w .  \\
nonempty~A\_27w{\unicdbdjdcd}{\unicdcdadad} A\_27x .  nonempty~A\_27x{\unicdbdjdcd}(({\unicdcdadad} V0f0 \in \\
((ty\_2Efcp\_2Ecart~2~A\_27x)^{{({{{ty\_2Efcp\_2Ecart}~{2}}~{A\_27w}})}}) .  ({\unicdcdadad} V1f \in \\
(ty\_2Ebinary\_\_ieee\_2Efloat~A\_27t~A\_27w) .  ((ap~(c\_2Ebinary\_\_ieee\_2Efloat\_\_Sign~\\
A\_27t~A\_27x)~(ap~(ap~(c\_2Ebinary\_\_ieee\_2Efloat\_\_Exponent\_\_fupd~\\
A\_27t~A\_27w~A\_27x)~V0f0)~V1f))=(ap~(c\_2Ebinary\_\_ieee\_2Efloat\_\_Sign~\\
A\_27t~A\_27w)~V1f)))){\unicdcdcdhd}(({\unicdcdadad} V2f0 \in ((ty\_2Efcp\_2Ecart~2~A\_27u)^{{({{{ty\_2Efcp\_2Ecart}~{2}}~{A\_27t}})}}) .  \\
({\unicdcdadad} V3f \in (ty\_2Ebinary\_\_ieee\_2Efloat~A\_27t~A\_27w) .  ((ap~(\\
c\_2Ebinary\_\_ieee\_2Efloat\_\_Sign~A\_27u~A\_27w)~(ap~(ap~(c\_2Ebinary\_\_ieee\_2Efloat\_\_Significand\_\_fupd~\\
A\_27t~A\_27u~A\_27w)~V2f0)~V3f))=(ap~(c\_2Ebinary\_\_ieee\_2Efloat\_\_Sign~\\
A\_27t~A\_27w)~V3f)))){\unicdcdcdhd}(({\unicdcdadad} V4f0 \in ((ty\_2Efcp\_2Ecart~2~ty\_2Eone\_2Eone)^{{({{{ty\_2Efcp\_2Ecart}~{2}}~{ty\_2Eone\_2Eone}})}}) .  \\
({\unicdcdadad} V5f \in (ty\_2Ebinary\_\_ieee\_2Efloat~A\_27t~A\_27w) .  ((ap~(\\
c\_2Ebinary\_\_ieee\_2Efloat\_\_Exponent~A\_27t~A\_27w)~(ap~(ap~(c\_2Ebinary\_\_ieee\_2Efloat\_\_Sign\_\_fupd~\\
A\_27t~A\_27w)~V4f0)~V5f))=(ap~(c\_2Ebinary\_\_ieee\_2Efloat\_\_Exponent~\\
A\_27t~A\_27w)~V5f)))){\unicdcdcdhd}(({\unicdcdadad} V6f0 \in ((ty\_2Efcp\_2Ecart~2~A\_27u)^{{({{{ty\_2Efcp\_2Ecart}~{2}}~{A\_27t}})}}) .  \\
({\unicdcdadad} V7f \in (ty\_2Ebinary\_\_ieee\_2Efloat~A\_27t~A\_27w) .  ((ap~(\\
c\_2Ebinary\_\_ieee\_2Efloat\_\_Exponent~A\_27u~A\_27w)~(ap~(ap~(c\_2Ebinary\_\_ieee\_2Efloat\_\_Significand\_\_fupd~\\
A\_27t~A\_27u~A\_27w)~V6f0)~V7f))=(ap~(c\_2Ebinary\_\_ieee\_2Efloat\_\_Exponent~\\
A\_27t~A\_27w)~V7f)))){\unicdcdcdhd}(({\unicdcdadad} V8f0 \in ((ty\_2Efcp\_2Ecart~2~ty\_2Eone\_2Eone)^{{({{{ty\_2Efcp\_2Ecart}~{2}}~{ty\_2Eone\_2Eone}})}}) .  \\
({\unicdcdadad} V9f \in (ty\_2Ebinary\_\_ieee\_2Efloat~A\_27t~A\_27w) .  ((ap~(\\
c\_2Ebinary\_\_ieee\_2Efloat\_\_Significand~A\_27t~A\_27w)~(ap~(ap~(\\
c\_2Ebinary\_\_ieee\_2Efloat\_\_Sign\_\_fupd~A\_27t~A\_27w)~V8f0)~V9f))=\\
(ap~(c\_2Ebinary\_\_ieee\_2Efloat\_\_Significand~A\_27t~A\_27w)~V9f)))){\unicdcdcdhd}\\
(({\unicdcdadad} V10f0 \in ((ty\_2Efcp\_2Ecart~2~A\_27x)^{{({{{ty\_2Efcp\_2Ecart}~{2}}~{A\_27w}})}}) .  \\
({\unicdcdadad} V11f \in (ty\_2Ebinary\_\_ieee\_2Efloat~A\_27t~A\_27w) .  ((ap~\\
(c\_2Ebinary\_\_ieee\_2Efloat\_\_Significand~A\_27t~A\_27x)~(ap~(ap~\\
(c\_2Ebinary\_\_ieee\_2Efloat\_\_Exponent\_\_fupd~A\_27t~A\_27w~A\_27x)~\\
V10f0)~V11f))=(ap~(c\_2Ebinary\_\_ieee\_2Efloat\_\_Significand~A\_27t~\\
A\_27w)~V11f)))){\unicdcdcdhd}(({\unicdcdadad} V12f0 \in ((ty\_2Efcp\_2Ecart~2~ty\_2Eone\_2Eone)^{{({{{ty\_2Efcp\_2Ecart}~{2}}~{ty\_2Eone\_2Eone}})}}) .  \\
({\unicdcdadad} V13f \in (ty\_2Ebinary\_\_ieee\_2Efloat~A\_27t~A\_27w) .  ((ap~\\
(c\_2Ebinary\_\_ieee\_2Efloat\_\_Sign~A\_27t~A\_27w)~(ap~(ap~(c\_2Ebinary\_\_ieee\_2Efloat\_\_Sign\_\_fupd~\\
A\_27t~A\_27w)~V12f0)~V13f))=(ap~V12f0~(ap~(c\_2Ebinary\_\_ieee\_2Efloat\_\_Sign~\\
A\_27t~A\_27w)~V13f))))){\unicdcdcdhd}(({\unicdcdadad} V14f0 \in ((ty\_2Efcp\_2Ecart~2~\\
A\_27x)^{{({{{ty\_2Efcp\_2Ecart}~{2}}~{A\_27w}})}}) .  ({\unicdcdadad} V15f \in (ty\_2Ebinary\_\_ieee\_2Efloat~\\
A\_27t~A\_27w) .  ((ap~(c\_2Ebinary\_\_ieee\_2Efloat\_\_Exponent~A\_27t~\\
A\_27x)~(ap~(ap~(c\_2Ebinary\_\_ieee\_2Efloat\_\_Exponent\_\_fupd~A\_27t~\\
A\_27w~A\_27x)~V14f0)~V15f))=(ap~V14f0~(ap~(c\_2Ebinary\_\_ieee\_2Efloat\_\_Exponent~\\
A\_27t~A\_27w)~V15f))))){\unicdcdcdhd}({\unicdcdadad} V16f0 \in ((ty\_2Efcp\_2Ecart~2~A\_27u)^{{({{{ty\_2Efcp\_2Ecart}~{2}}~{A\_27t}})}}) .  \\
({\unicdcdadad} V17f \in (ty\_2Ebinary\_\_ieee\_2Efloat~A\_27t~A\_27w) .  ((ap~\\
(c\_2Ebinary\_\_ieee\_2Efloat\_\_Significand~A\_27u~A\_27w)~(ap~(ap~\\
(c\_2Ebinary\_\_ieee\_2Efloat\_\_Significand\_\_fupd~A\_27t~A\_27u~A\_27w)~\\
V16f0)~V17f))=(ap~V16f0~(ap~(c\_2Ebinary\_\_ieee\_2Efloat\_\_Significand~\\
A\_27t~A\_27w)~V17f)))))))))))))\end{array}
\label{hyp:ehigngpfcdfecgjgogbgchjhpfpfjgfgfgfgpfcdfeggmgpgbgehpfpfbgdgdgggfhahegdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} A\_27t .  nonempty~A\_27t{\unicdbdjdcd}{\unicdcdadad} A\_27w .  nonempty~A\_27w{\unicdbdjdcd}(\\
{\unicdcdadad} V0f1 \in (ty\_2Ebinary\_\_ieee\_2Efloat~A\_27t~A\_27w) .  ({\unicdcdadad} V1f2 \in \\
(ty\_2Ebinary\_\_ieee\_2Efloat~A\_27t~A\_27w) .  ((V0f1=V1f2){\unicdbdjded}(((ap~\\
(c\_2Ebinary\_\_ieee\_2Efloat\_\_Sign~A\_27t~A\_27w)~V0f1)=(ap~(c\_2Ebinary\_\_ieee\_2Efloat\_\_Sign~\\
A\_27t~A\_27w)~V1f2)){\unicdcdcdhd}(((ap~(c\_2Ebinary\_\_ieee\_2Efloat\_\_Exponent~\\
A\_27t~A\_27w)~V0f1)=(ap~(c\_2Ebinary\_\_ieee\_2Efloat\_\_Exponent~\\
A\_27t~A\_27w)~V1f2)){\unicdcdcdhd}((ap~(c\_2Ebinary\_\_ieee\_2Efloat\_\_Significand~\\
A\_27t~A\_27w)~V0f1)=(ap~(c\_2Ebinary\_\_ieee\_2Efloat\_\_Significand~\\
A\_27t~A\_27w)~V1f2)))))))\end{array}
\label{hyp:ehigngpfcdfecgjgogbgchjhpfpfjgfgfgfgpfcdfeggmgpgbgehpfpfdgpgngahpgogfgogehpfpffgbhfhbgmgjgehjh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} A\_27a .  nonempty~A\_27a{\unicdbdjdcd}{\unicdcdadad} A\_27b .  nonempty~A\_27b{\unicdbdjdcd}(\\
{\unicdcdadad} V0x \in A\_27a .  ({\unicdcdadad} V1y \in A\_27b .  ((ap~(ap~(\mname{c\_2Ecombin\_2EK}~\\
A\_27a~A\_27b)~V0x)~V1y)=V0x)))\end{array}
\label{hyp:ehigngpfcdfedgpgngcgjgogpfcdfelepfpfefiene}
\end{equation}
\begin{theorem}\label{thm:ehigngpfcdfecgjgogbgchjhpfpfjgfgfgfgpfcdfeggmgpgbgehpfpfmgjgehfgchbgmgpfpfbdbd}
$$\begin{array}{c}{\unicdcdadad} A\_27t .  nonempty~A\_27t{\unicdbdjdcd}{\unicdcdadad} A\_27u .  nonempty~A\_27u{\unicdbdjdcd}{\unicdcdadad} A\_27w .  \\
nonempty~A\_27w{\unicdbdjdcd}{\unicdcdadad} A\_27x .  nonempty~A\_27x{\unicdbdjdcd}({\unicdcdadad} V0c11 \in \\
(ty\_2Efcp\_2Ecart~2~ty\_2Eone\_2Eone) .  ({\unicdcdadad} V1c01 \in (ty\_2Efcp\_2Ecart~\\
2~A\_27x) .  ({\unicdcdadad} V2c1 \in (ty\_2Efcp\_2Ecart~2~A\_27u) .  ({\unicdcdadad} V3c12 \in \\
(ty\_2Efcp\_2Ecart~2~ty\_2Eone\_2Eone) .  ({\unicdcdadad} V4c02 \in (ty\_2Efcp\_2Ecart~\\
2~A\_27x) .  ({\unicdcdadad} V5c2 \in (ty\_2Efcp\_2Ecart~2~A\_27u) .  (((ap~(ap~\\
(c\_2Ebinary\_\_ieee\_2Efloat\_\_Sign\_\_fupd~A\_27u~A\_27x)~(ap~(\mname{c\_2Ecombin\_2EK}~\\
(ty\_2Efcp\_2Ecart~2~ty\_2Eone\_2Eone)~(ty\_2Efcp\_2Ecart~2~ty\_2Eone\_2Eone))~\\
V0c11))~(ap~(ap~(c\_2Ebinary\_\_ieee\_2Efloat\_\_Exponent\_\_fupd~A\_27u~\\
A\_27w~A\_27x)~(ap~(\mname{c\_2Ecombin\_2EK}~(ty\_2Efcp\_2Ecart~2~A\_27x)~(ty\_2Efcp\_2Ecart~\\
2~A\_27w))~V1c01))~(ap~(ap~(c\_2Ebinary\_\_ieee\_2Efloat\_\_Significand\_\_fupd~\\
A\_27t~A\_27u~A\_27w)~(ap~(\mname{c\_2Ecombin\_2EK}~(ty\_2Efcp\_2Ecart~2~A\_27u)~\\
(ty\_2Efcp\_2Ecart~2~A\_27t))~V2c1))~(c\_2Ebool\_2EARB~(ty\_2Ebinary\_\_ieee\_2Efloat~\\
A\_27t~A\_27w)))))=(ap~(ap~(c\_2Ebinary\_\_ieee\_2Efloat\_\_Sign\_\_fupd~\\
A\_27u~A\_27x)~(ap~(\mname{c\_2Ecombin\_2EK}~(ty\_2Efcp\_2Ecart~2~ty\_2Eone\_2Eone)~\\
(ty\_2Efcp\_2Ecart~2~ty\_2Eone\_2Eone))~V3c12))~(ap~(ap~(c\_2Ebinary\_\_ieee\_2Efloat\_\_Exponent\_\_fupd~\\
A\_27u~A\_27w~A\_27x)~(ap~(\mname{c\_2Ecombin\_2EK}~(ty\_2Efcp\_2Ecart~2~A\_27x)~\\
(ty\_2Efcp\_2Ecart~2~A\_27w))~V4c02))~(ap~(ap~(c\_2Ebinary\_\_ieee\_2Efloat\_\_Significand\_\_fupd~\\
A\_27t~A\_27u~A\_27w)~(ap~(\mname{c\_2Ecombin\_2EK}~(ty\_2Efcp\_2Ecart~2~A\_27u)~\\
(ty\_2Efcp\_2Ecart~2~A\_27t))~V5c2))~(c\_2Ebool\_2EARB~(ty\_2Ebinary\_\_ieee\_2Efloat~\\
A\_27t~A\_27w)))))){\unicdbdjded}((V0c11=V3c12){\unicdcdcdhd}((V1c01=V4c02){\unicdcdcdhd}(V2c1=V5c2))))))))))\end{array}$$
\end{theorem}
\end{document}
