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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="coh_sp.html#K21" target="_self">MapsT</a> <font color="Maroon">c<sub>1</sub></font>;<br/>



<a NAME="E1:65"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Olive">b<sub>3</sub></font></span><a href="tarski.html#K4">]</a></span> where B is    <a href="subset_1.html#M1">Element</a> of  <a href="coh_sp.html#K17" target="_self">TOL</a> <font color="Maroon">c<sub>1</sub></font>, B is    <a href="subset_1.html#M1">Element</a> of  <a href="coh_sp.html#K17" target="_self">TOL</a> <font color="Maroon">c<sub>1</sub></font>, B is    <a href="subset_1.html#M1">Element</a> of  <a href="coh_sp.html#K20" target="_self">FuncsT</a> <font color="Maroon">c<sub>1</sub></font> : ( ( <font color="Olive">b<sub>2</sub></font> <a href="coh_sp.html#K18" target="_self">`2</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  implies <font color="Olive">b<sub>1</sub></font> <a href="coh_sp.html#K18" target="_self">`2</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  ) &amp; <font color="Olive">b<sub>3</sub></font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Olive">b<sub>1</sub></font> <a href="coh_sp.html#K18" target="_self">`2</a> ,<font color="Olive">b<sub>2</sub></font> <a href="coh_sp.html#K18" target="_self">`2</a>  &amp; ( for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="hidden.html#M1">set</a>  st <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>5</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> <a href="coh_sp.html#K19" target="_self">`1</a>  holds <br/><span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>5</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>2</sub></font> <a href="coh_sp.html#K19" target="_self">`1</a>  ) ) </span>}</span> 
 
;<br/>
<a NAME="E2:65"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="coh_sp.html#K17" target="_self">TOL</a> <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>3</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="coh_sp.html#K20" target="_self">FuncsT</a> <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Olive">b<sub>3</sub></font></span><a href="tarski.html#K4">]</a></span> &amp; ( <font color="Olive">b<sub>2</sub></font> <a href="coh_sp.html#K18" target="_self">`2</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  implies <font color="Olive">b<sub>1</sub></font> <a href="coh_sp.html#K18" target="_self">`2</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  ) &amp; <font color="Olive">b<sub>3</sub></font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Olive">b<sub>1</sub></font> <a href="coh_sp.html#K18" target="_self">`2</a> ,<font color="Olive">b<sub>2</sub></font> <a href="coh_sp.html#K18" target="_self">`2</a>  &amp; ( for <font color="Olive">b<sub>4</sub></font>, <font color="Olive">b<sub>5</sub></font> being   <a href="hidden.html#M1">set</a>  st <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>5</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> <a href="coh_sp.html#K19" target="_self">`1</a>  holds <br/><span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>5</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>2</sub></font> <a href="coh_sp.html#K19" target="_self">`1</a>  ) )
 
;<br/>
<b>hence </b><a NAME="E3:65"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="coh_sp.html#K20" target="_self">FuncsT</a> <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="coh_sp.html#K17" target="_self">TOL</a> <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Olive">b<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span> &amp; ( <font color="Olive">b<sub>3</sub></font> <a href="coh_sp.html#K18" target="_self">`2</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  implies <font color="Olive">b<sub>2</sub></font> <a href="coh_sp.html#K18" target="_self">`2</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  ) &amp; <font color="Olive">b<sub>1</sub></font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Olive">b<sub>2</sub></font> <a href="coh_sp.html#K18" target="_self">`2</a> ,<font color="Olive">b<sub>3</sub></font> <a href="coh_sp.html#K18" target="_self">`2</a>  &amp; ( for <font color="Olive">b<sub>4</sub></font>, <font color="Olive">b<sub>5</sub></font> being   <a href="hidden.html#M1">set</a>  st <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>5</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>2</sub></font> <a href="coh_sp.html#K19" target="_self">`1</a>  holds <br/><span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>5</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>3</sub></font> <a href="coh_sp.html#K19" target="_self">`1</a>  ) )
 ;<br/>


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