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<span class="kw">let </span><font color="Maroon" title="c3">f</font>, <font color="Maroon" title="c4">g</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="card_3.html#D10" onmouseover="rs('card_3/D10')" onmouseout="rh()">CARD_3:def 10</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c3">f</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="compos_0.html#K6" title="COMPOS_0:func.6">JumpParts</a> <font color="Maroon" title="c2">T</font> or  not <font color="Maroon" title="c4">g</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="compos_0.html#K6" title="COMPOS_0:func.6">JumpParts</a> <font color="Maroon" title="c2">T</font> or  <a href="xtuple_0.html#K9" title="XTUPLE_0:func.9">proj1</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xtuple_0.html#K9" title="XTUPLE_0:func.9">proj1</a> <font color="Maroon" title="c4">g</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:20_1_1"/><span class="lab"><font color="Green" title="E5">A1</font></span>: 
<font color="Maroon" title="c3">f</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="compos_0.html#K6" title="COMPOS_0:func.6">JumpParts</a> <font color="Maroon" title="c2">T</font>
 <span class="kw">and </span><br/><a NAME="E2:20_1_1"/><span class="lab"><font color="Green" title="E6">A2</font></span>: 
<font color="Maroon" title="c4">g</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="compos_0.html#K6" title="COMPOS_0:func.6">JumpParts</a> <font color="Maroon" title="c2">T</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="xtuple_0.html#K9" title="XTUPLE_0:func.9">proj1</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xtuple_0.html#K9" title="XTUPLE_0:func.9">proj1</a> <font color="Maroon" title="c4">g</font></span><br/>

<a NAME="E3:20_1_1"/><span class="lab"><font color="Green" title="E7">A3</font></span>: 
 ex <font color="Olive" title="b1">I</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">S</font> st <br/>( <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Olive" title="b1">I</font> &amp;  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Olive" title="b1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">T</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:20_1_1"><span class="lab"><font color="Green" title="E5">A1</font></span></a></span>;<br/>
<a NAME="E4:20_1_1"/>
 ex <font color="Olive" title="b1">J</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">S</font> st <br/>( <font color="Maroon" title="c4">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Olive" title="b1">J</font> &amp;  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Olive" title="b1">J</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">T</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:20_1_1"><span class="lab"><font color="Green" title="E6">A2</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:20_1_1"/>
 <a href="xtuple_0.html#K9" title="XTUPLE_0:func.9">proj1</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xtuple_0.html#K9" title="XTUPLE_0:func.9">proj1</a> <font color="Maroon" title="c4">g</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:20_1_1"><span class="lab"><font color="Green" title="E7">A3</font></span></a>, <a class="ref" href="compos_0.html#D5" target="_self" onmouseover="rs('compos_0/D5')" onmouseout="rh()">Def5</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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