\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{t61\_comptrig (TMLE1dViLoz9gPF5EPdxYhD2QdYvt4VSfQr)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k20\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k8\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k32\_sin\_cos : {\iota}$ be given.
Let $ k21\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k18\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_square\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k17\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_0 : {\iota}$ be given.
Let $ k4\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k31\_sin\_cos : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}(k21\_sin\_cos~(k10\_real\_1~k32\_sin\_cos~np\_\_2)=k6\_numbers){\unicdcdcdhd}((\\
k18\_sin\_cos~(k10\_real\_1~k32\_sin\_cos~np\_\_2)=np\_\_1){\unicdcdcdhd}((k21\_sin\_cos~\\
k32\_sin\_cos=k1\_real\_1~np\_\_1){\unicdcdcdhd}((k18\_sin\_cos~k32\_sin\_cos=k6\_numbers){\unicdcdcdhd}\\
((k21\_sin\_cos~(k7\_real\_1~k32\_sin\_cos~(k10\_real\_1~k32\_sin\_cos~\\
np\_\_2))=k6\_numbers){\unicdcdcdhd}((k18\_sin\_cos~(k7\_real\_1~k32\_sin\_cos~(\\
k10\_real\_1~k32\_sin\_cos~np\_\_2))=k1\_real\_1~np\_\_1){\unicdcdcdhd}((k21\_sin\_cos~\\
(k8\_real\_1~np\_\_2~k32\_sin\_cos)=np\_\_1){\unicdcdcdhd}(k18\_sin\_cos~(k8\_real\_1~\\
np\_\_2~k32\_sin\_cos)=k6\_numbers)))))))\end{array}
\label{hyp:ehhdhdpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{{{k3\_xcmplx\_0}~{np\_\_1}}~{X0}}={X0}})}}}\label{hyp:ehddpfbgchjgehigng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((k2\_xcmplx\_0~(k3\_square\_1~(k20\_sin\_cos~\\
X0))~(k3\_square\_1~(k17\_sin\_cos~X0))=np\_\_1){\unicdcdcdhd}(k2\_xcmplx\_0~(k3\_xcmplx\_0~\\
(k20\_sin\_cos~X0)~(k20\_sin\_cos~X0))~(k3\_xcmplx\_0~(k17\_sin\_cos~\\
X0)~(k17\_sin\_cos~X0))=np\_\_1))\end{array}
\label{hyp:ehcdjdpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{{{k2\_xcmplx\_0}~{X0}}~{k6\_numbers}}={X0}})}}}\label{hyp:ehbdpfbgchjgehigng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}(\preoh (r1\_xxreal\_0~k6\_numbers~X0){\unicdcdcdhd}((\\
\preoh r1\_xxreal\_0~(k8\_real\_1~np\_\_2~k32\_sin\_cos)~X0){\unicdcdcdhd}((k17\_sin\_cos~\\
X0=k6\_numbers){\unicdcdcdhd}((X0{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}(X0{\unicdcdgdad}k32\_sin\_cos)))))\end{array}
\label{hyp:ehbdhdpfdgpgngahehchjghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_xcmplx\_0~X0){\unicdcdcdhd}((v1\_xcmplx\_0~\\
X1){\unicdcdcdhd}(v1\_xcmplx\_0~X2))){\unicdbdjdcd}(k2\_xcmplx\_0~(k2\_xcmplx\_0~X0~X1)~X2=k2\_xcmplx\_0~\\
X0~(k2\_xcmplx\_0~X1~X2))\end{array}
\label{hyp:dhahdggdpfbgchjgehigng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{np\_\_0}}\label{hyp:dhahdgadpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{{{k3\_xcmplx\_0}~{np\_\_1}}~{np\_\_1}}={np\_\_1}}\label{hyp:chbhcffgbgmgnefhmgehpfpflgddpfihdgngahmgihpfadpfpfchbdpfchbdpfchbd}
\end{equation}
Assume the following.
\begin{equation}
{{{{k2\_xcmplx\_0}~{({{k4\_xcmplx\_0}~{np\_\_1}})}}~{np\_\_1}}={np\_\_0}}\label{hyp:chbhcffgbgmgbeegegpfpflgcdpfihdgngahmgihpfadpfpfchngbdpfchbdpfchad}
\end{equation}
Assume the following.
\begin{equation}
{{{r1\_xxreal\_0}~{({{k4\_xcmplx\_0}~{np\_\_1}})}}~{np\_\_0}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchngbdpfchad}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_1}}~{np\_\_0}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdpfchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k1\_numbers){\unicdcdcdhd}(v1\_xreal\_0~\\
X1)){\unicdbdjdcd}(k8\_real\_1~X0~X1=k3\_xcmplx\_0~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{k32\_sin\_cos}={k31\_sin\_cos}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgddcdpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(k21\_sin\_cos~X0=k20\_sin\_cos~\\
X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdbdpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{{k1\_real\_1}~{X0}}={{k4\_xcmplx\_0}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(k18\_sin\_cos~X0=k17\_sin\_cos~\\
X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdidpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_xcmplx\_0~X0)){\unicdcdcdhd}\\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(v1\_xcmplx\_0~X1))){\unicdbdjdcd}(\preoh v1\_xboole\_0~(k3\_xcmplx\_0~\\
X0~X1))\end{array}
\label{hyp:ggdgidpfihdgngahmgihpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xcmplx\_0~X0){\unicdcdcdhd}(v1\_xcmplx\_0~X1)){\unicdbdjdcd}(\\
v1\_xcmplx\_0~(k3\_xcmplx\_0~X0~X1))\end{array}
\label{hyp:ggdgddpfihdgngahmgihpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k1\_numbers){\unicdcdcdhd}(v1\_xreal\_0~\\
X1)){\unicdbdjdcd}(m1\_subset\_1~(k8\_real\_1~X0~X1)~k1\_numbers)\end{array}
\label{hyp:egehpflgidpfchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k32\_sin\_cos}}~{k1\_numbers}}\label{hyp:egehpflgddcdpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(m1\_subset\_1~(k21\_sin\_cos~\\
X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgcdbdpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(m1\_subset\_1~(k18\_sin\_cos~\\
X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdidpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{{k3\_square\_1}~{X0}}={{{k3\_xcmplx\_0}~{X0}}~{X0}}})}}}\label{hyp:egbdpfdhbhfhbgchfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xcmplx\_0~X0){\unicdcdcdhd}(v1\_xcmplx\_0~X1)){\unicdbdjdcd}(\\
k2\_xcmplx\_0~X0~X1=k2\_xcmplx\_0~X1~X0)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfihdgngahmgihpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgddpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgbdpfihdgngahmgihpfad}
\end{equation}
\begin{theorem}\label{thm:ehgdbdpfdgpgngahehchjghg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}(((r1\_xxreal\_0~k6\_numbers~X0){\unicdcdcdhd}(k20\_sin\_cos~\\
X0=np\_\_1)){\unicdbdjdcd}((r1\_xxreal\_0~(k8\_real\_1~np\_\_2~k32\_sin\_cos)~X0){\unicdcdcdid}\\
(X0=k6\_numbers)))\end{array}$$
\end{theorem}
\end{document}
