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<span class="kw">set </span><font color="Maroon" title="c3">f</font> = <font color="Maroon" title="c1">fi</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c2">psi</font>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c4">A1</font> being   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a><span class="kw"> such that </span><br/><a NAME="E2:5_1_1"/><span class="lab"><font color="Green" title="E6">A1</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">fi</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">A1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal2.html#D8" title="ORDINAL2:def.8">ORDINAL2:def 8</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c5">A2</font> being   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a><span class="kw"> such that </span><br/><a NAME="E4:5_1_1"/><span class="lab"><font color="Green" title="E7">A2</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">psi</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">A2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal2.html#D8" title="ORDINAL2:def.8">ORDINAL2:def 8</a></span>;<br/>
<a NAME="E5:5_1_1"/><span class="lab"><font color="Green" title="E8">A4</font></span>: 
<font color="Maroon" title="c5">A2</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c4">A1</font> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Maroon" title="c5">A2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal3.html#T27" title="ORDINAL3:th.27">ORDINAL3:27</a></span>;<br/>
<a NAME="E6:5_1_1"/>
<font color="Maroon" title="c4">A1</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c4">A1</font> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Maroon" title="c5">A2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal3.html#T27" title="ORDINAL3:th.27">ORDINAL3:27</a></span>;<br/>
<a NAME="E7:5_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E9">X1</font></span>: 
<font color="Maroon" title="c4">A1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c5">A2</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c4">A1</font> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Maroon" title="c5">A2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:5_1_1"><span class="lab"><font color="Green" title="E8">A4</font></span></a>, <a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></span>;<br/>
<a NAME="E8:5_1_1"/><span class="lab"><font color="Green" title="E10">X2</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">fi</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c2">psi</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">fi</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">psi</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal4.html#T2" target="_self" title="ORDINAL4:th.2">Th2</a></span>;<br/>
<a NAME="E9:5_1_1"/>
<span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">fi</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">psi</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">A1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c5">A2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:5_1_1"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="txt" href="#E4:5_1_1"><span class="lab"><font color="Green" title="E7">A2</font></span></a>, <a class="ref" href="xboole_1.html#T13" title="XBOOLE_1:th.13">XBOOLE_1:13</a></span>;<br/>
<a NAME="E10:5_1_1"/><span class="kw">then </span>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">fi</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c2">psi</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">A1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c5">A2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:5_1_1"><span class="lab"><font color="Green" title="E10">X2</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<a NAME="E11:5_1_1"/><span class="kw">then </span>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">fi</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c2">psi</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">A1</font> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Maroon" title="c5">A2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:5_1_1"><span class="lab"><font color="Green" title="E9">X1</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:5_1_1"/>
<font color="Maroon" title="c1">fi</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c2">psi</font> is  <a href="ordinal2.html#V1" title="ORDINAL2:attr.1">Ordinal-yielding</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal2.html#D8" title="ORDINAL2:def.8">ORDINAL2:def 8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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