<?xml version="1.0"?>
<div class="add">

<span class="kw">take </span><font color="Maroon" title="c2">f</font> = <font color="Maroon" title="c1">I</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</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"> <font color="Maroon" title="c2">f</font> is  <a href="msafree5.html#V6" title="MSAFREE5:attr.6">infinite-yielding</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">J</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="msafree5.html#D8" target="_self" onmouseover="rs('msafree5/D8')" onmouseout="rh()">MSAFREE5:def 8</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"> ( <font color="Maroon" title="c3">J</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">rng</a> <font color="Maroon" title="c2">f</font> implies <font color="Maroon" title="c3">J</font> is  <a href="finset_1.html#NV2" title="FINSET_1:NV.2">infinite</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:19_1_1"/><span class="lab"><font color="Green" title="E11">A1</font></span>: 
<font color="Maroon" title="c3">J</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c2">f</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"> <font color="Maroon" title="c3">J</font> is  <a href="finset_1.html#NV2" title="FINSET_1:NV.2">infinite</a> </span><br/>

<a NAME="E2:19_1_1"/>
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c2">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T13" onmouseover="rs('funcop_1/T13')" onmouseout="rh()">FUNCOP_1:13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:19_1_1"/>
<font color="Maroon" title="c3">J</font> is  <a href="finset_1.html#NV2" title="FINSET_1:NV.2">infinite</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19_1_1"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</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/>


</div>
