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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">c<sub>3</sub></font> <a href="yellow_1.html#K6">|^</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="yellow_0.html#M1">SubRelStr</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="yellow_1.html#K6">|^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="yellow_1.html#K6">|^</a> <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font>;<br/>









<b>assume </b><a NAME="E1:2"/><i><font color="Green">E4</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> is <a href="waybel27.html#V1">uncurrying</a> &amp; <font color="Maroon">c<sub>6</sub></font> is <a href="funct_1.html#V2">one-to-one</a> &amp; <font color="Maroon">c<sub>6</sub></font> is <a href="funct_2.html#V2">onto</a> )
 ;<br/>

<a NAME="E2:2"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> <a href="tops_2.html#NK3" target="_self">"</a>  is <a href="funct_1.html#V2">one-to-one</a> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="tops_2.html#NK3" target="_self">"</a>  is <a href="funct_2.html#V2">onto</a> )
 
<b>by </b><i><a class="ref" href="waybel29.html#T1" target="_self">Th1</a></i>;<br/>
<a NAME="E3:2"/><b>then </b><i><font color="Green">E5</font></i>: 
(  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="txt" href="waybel29.html#E1:2"><i><font color="Green">E4</font></i></a>, <a class="ref" href="funct_2.html#D3">FUNCT_2:def 3</a></i>;<br/>
<a NAME="E4:2"/><i><font color="Green">E6</font></i>: 
(  <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="yellow_1.html#K6">|^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="yellow_1.html#K6">|^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="yellow_1.html#K6">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp;  <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">c<sub>2</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="yellow_1.html#K6">|^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp;  <a href="funct_2.html#K1">Funcs</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="yellow_1.html#K6">|^</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> )
 
<b>by </b><i><a class="ref" href="yellow_1.html#T28">YELLOW_1:28</a></i>;<br/>
<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="waybel27.html#D2">WAYBEL27:def 2</a>
<div class="add"><b>let </b><font color="Maroon">c<sub>7</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:2_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span>
 ;<br/><a NAME="E2:2_1"/><b>then </b>
<font color="Maroon">c<sub>7</sub></font> is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="yellow_1.html#K6">|^</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="yellow_0.html#T59">YELLOW_0:59</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>7</sub></font> as   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> <b>by </b><i><a class="txt" href="waybel29.html#E4:2"><i><font color="Green">E6</font></i></a>, <a class="ref" href="funct_2.html#T121">FUNCT_2:121</a></i>;<br/><a NAME="E4:2_1"/>
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a>  <a href="funct_5.html#K1">proj1</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="funct_5.html#T21">FUNCT_5:21</a></i>;<br/><b>hence </b><a NAME="E5:2_1"/>
( <font color="Maroon">c<sub>7</sub></font> is   <a href="funct_1.html#NM1">Function</a> &amp;  <a href="funct_5.html#K1">proj1</a> <font color="Maroon">c<sub>7</sub></font> is   <a href="relat_1.html#NM1">Relation</a> )
 ;<br/></div>
<b>end;</b></div>

<a NAME="E6:2"/>
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font>
 
;<br/>
<a NAME="E7:2"/><b>then </b><i><font color="Green">E7</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="tops_2.html#NK3" target="_self">"</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K2">"</a> 
 
<b>by </b><i><a class="txt" href="waybel29.html#E1:2"><i><font color="Green">E4</font></i></a>, <a class="txt" href="waybel29.html#E3:2"><i><font color="Green">E5</font></i></a>, <a class="ref" href="tops_2.html#D4">TOPS_2:def 4</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>7</sub></font> be   <a href="funct_1.html#NM1">Function</a>;<br/>

<b>assume </b><a NAME="E8:2"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>8</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E10:2"/><i><font color="Green">E8</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font> )
 <b>by </b><i><a class="txt" href="waybel29.html#E3:2"><i><font color="Green">E5</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>8</sub></font> as   <a href="funct_1.html#NM1">Function</a> <b>by </b><i><a class="txt" href="waybel29.html#E1:2"><i><font color="Green">E4</font></i></a>, <a class="txt" href="waybel29.html#E10:2"><i><font color="Green">E8</font></i></a>, <a class="ref" href="waybel27.html#D1">WAYBEL27:def 1</a></i>;<br/>
<a NAME="E12:2"/><i><font color="Green">E9</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="funct_5.html#K4">uncurry</a> <font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="txt" href="waybel29.html#E1:2"><i><font color="Green">E4</font></i></a>, <a class="txt" href="waybel29.html#E10:2"><i><font color="Green">E8</font></i></a>, <a class="ref" href="waybel27.html#D1">WAYBEL27:def 1</a></i>;<br/>
<a NAME="E13:2"/>
<font color="Maroon">c<sub>9</sub></font> is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="yellow_1.html#K6">|^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="yellow_1.html#K6">|^</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="waybel29.html#E10:2"><i><font color="Green">E8</font></i></a>, <a class="ref" href="yellow_0.html#T59">YELLOW_0:59</a></i>;<br/>
<a NAME="E14:2"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">c<sub>1</sub></font>, <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">c<sub>2</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="waybel29.html#E4:2"><i><font color="Green">E6</font></i></a>, <a class="ref" href="funct_2.html#T121">FUNCT_2:121</a></i>;<br/>
<a NAME="E15:2"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>9</sub></font> <a href="tarski.html#R1">c=</a>  <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">c<sub>2</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="relset_1.html#T12">RELSET_1:12</a></i>;<br/>
<a NAME="E16:2"/><b>then </b>
 <a href="funct_5.html#K3">curry</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="txt" href="waybel29.html#E12:2"><i><font color="Green">E9</font></i></a>, <a class="ref" href="funct_5.html#T55">FUNCT_5:55</a></i>;<br/>
<b>hence </b><a NAME="E17:2"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="tops_2.html#NK3" target="_self">"</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="funct_5.html#K3">curry</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="waybel29.html#E1:2"><i><font color="Green">E4</font></i></a>, <a class="txt" href="waybel29.html#E7:2"><i><font color="Green">E7</font></i></a>, <a class="txt" href="waybel29.html#E10:2"><i><font color="Green">E8</font></i></a>, <a class="ref" href="funct_1.html#T54">FUNCT_1:54</a></i>;<br/>


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