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<b>let </b><font color="Maroon">G1</font> be  non <a href="struct_0.html#V3">empty</a> <a href="lang1.html#V1">strict</a>  <a href="lang1.html#L1">DTConstrStr</a> , <font color="Maroon">G2</font> be  non <a href="struct_0.html#V3">empty</a> <a href="lang1.html#V1">strict</a>  <a href="lang1.html#L1">DTConstrStr</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:15_1"/><i><font color="Green">E31</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>1</sub></font>() &amp; ( for <font color="Olive">x</font> being  <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">G1</font><br/> for <font color="Olive">p</font> being   <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G1</font> holds <br/> ( <font color="Olive">x</font> <a href="lang1.html#R1">==&gt;</a> <font color="Olive">p</font> iff <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">x</font>,<font color="Olive">p</font>] ) ) )
 <b>and </b><br/><a NAME="E2:15_1"/><i><font color="Green">E32</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>1</sub></font>() &amp; ( for <font color="Olive">x</font> being  <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">G2</font><br/> for <font color="Olive">p</font> being   <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G2</font> holds <br/> ( <font color="Olive">x</font> <a href="lang1.html#R1">==&gt;</a> <font color="Olive">p</font> iff <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">x</font>,<font color="Olive">p</font>] ) ) )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:15_1_1_1"/><i><font color="Green">E34</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="lang1.html#U1">Rules</a> of <font color="Maroon">G1</font>
 ;<br/><a NAME="E2:15_1_1_1"/><b>then </b><i><font color="Green">E45</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G1</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G1</font> <a href="finseq_2.html#K3">*</a>  )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/><b>reconsider </b><font color="Maroon">x1</font> = <font color="Maroon">x</font> as   <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">G1</font> <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/><b>reconsider </b><font color="Maroon">y1</font> = <font color="Maroon">y</font> as    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G1</font> <b>by </b><i>, <a class="ref" href="finseq_2.html#D3">FINSEQ_2:def 3</a></i>;<br/><a NAME="E5:15_1_1_1"/><i><font color="Green">E59</font></i>: 
( <font color="Maroon">x1</font> <a href="lang1.html#R1">==&gt;</a> <font color="Maroon">y1</font> iff <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">x1</font>,<font color="Maroon">y1</font>] )
 <b>by </b><i/>;<br/><b>reconsider </b><font color="Maroon">x2</font> = <font color="Maroon">x</font> as   <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">G2</font> <b>by </b><i>, , , <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/><b>reconsider </b><font color="Maroon">y2</font> = <font color="Maroon">y</font> as    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G2</font> <b>by </b><i>, , , <a class="ref" href="finseq_2.html#D3">FINSEQ_2:def 3</a></i>;<br/><a NAME="E8:15_1_1_1"/>
<font color="Maroon">x2</font> <a href="lang1.html#R1">==&gt;</a> <font color="Maroon">y2</font>
 <b>by </b><i>, , , <a class="ref" href="lang1.html#D1">LANG1:def 1</a></i>;<br/><b>hence </b><a NAME="E9:15_1_1_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="lang1.html#U1">Rules</a> of <font color="Maroon">G2</font>
 <b>by </b><i><a class="ref" href="lang1.html#D1">LANG1:def 1</a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:15_1_1"/><i><font color="Green">E62</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="lang1.html#U1">Rules</a> of <font color="Maroon">G2</font>
 ;<br/><a NAME="E3:15_1_1"/><b>then </b><i><font color="Green">E63</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G2</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G2</font> <a href="finseq_2.html#K3">*</a>  )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/><b>reconsider </b><font color="Maroon">x2</font> = <font color="Maroon">x</font> as   <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">G2</font> <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/><b>reconsider </b><font color="Maroon">y2</font> = <font color="Maroon">y</font> as    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G2</font> <b>by </b><i>, <a class="ref" href="finseq_2.html#D3">FINSEQ_2:def 3</a></i>;<br/><a NAME="E6:15_1_1"/><i><font color="Green">E64</font></i>: 
( <font color="Maroon">x2</font> <a href="lang1.html#R1">==&gt;</a> <font color="Maroon">y2</font> iff <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">x2</font>,<font color="Maroon">y2</font>] )
 <b>by </b><i/>;<br/><b>reconsider </b><font color="Maroon">x1</font> = <font color="Maroon">x</font> as   <a href="lang1.html#NM1">Symbol</a> of <font color="Maroon">G1</font> <b>by </b><i>, , , <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/><b>reconsider </b><font color="Maroon">y1</font> = <font color="Maroon">y</font> as    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G1</font> <b>by </b><i>, , , <a class="ref" href="finseq_2.html#D3">FINSEQ_2:def 3</a></i>;<br/><a NAME="E9:15_1_1"/>
<font color="Maroon">x1</font> <a href="lang1.html#R1">==&gt;</a> <font color="Maroon">y1</font>
 <b>by </b><i>, , , <a class="ref" href="lang1.html#D1">LANG1:def 1</a></i>;<br/><b>hence </b><a NAME="E10:15_1_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="lang1.html#U1">Rules</a> of <font color="Maroon">G1</font>
 <b>by </b><i><a class="ref" href="lang1.html#D1">LANG1:def 1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:15_1"/>
<font color="Maroon">G1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G2</font>
 <b>by </b><i>, , <a class="ref" href="relat_1.html#D2">RELAT_1:def 2</a></i>;<br/>


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