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<span class="kw">let </span><font color="Maroon" title="c1">S1</font>, <font color="Maroon" title="c2">S2</font> be   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">T-Sequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">S1</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c2">S2</font> is  <a href="ordinal2.html#V1" title="ORDINAL2:attr.1">Ordinal-yielding</a>  implies ( <font color="Maroon" title="c1">S1</font> is  <a href="ordinal2.html#V1" title="ORDINAL2:attr.1">Ordinal-yielding</a>  &amp; <font color="Maroon" title="c2">S2</font> is  <a href="ordinal2.html#V1" title="ORDINAL2:attr.1">Ordinal-yielding</a>  ) )</span><br/>



<span class="kw">given </span><font color="Maroon" title="c3">a</font> being   <a href="ordinal1.html#V3" title="ORDINAL1:attr.3">ordinal</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> <span class="kw"> such that </span><a NAME="E2:7"/><span class="lab"><font color="Green" title="E5">A0</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">S1</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c2">S2</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">a</font>
 ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="ordinal2.html#D8" title="ORDINAL2:def.8">ORDINAL2:def 8</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">S1</font> is  <a href="ordinal2.html#V1" title="ORDINAL2:attr.1">Ordinal-yielding</a>  &amp; <font color="Maroon" title="c2">S2</font> is  <a href="ordinal2.html#V1" title="ORDINAL2:attr.1">Ordinal-yielding</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E3:7"/>
<font color="Maroon" title="c1">S1</font> is  <a href="ordinal2.html#V1" title="ORDINAL2:attr.1">Ordinal-yielding</a> 
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">S2</font> is  <a href="ordinal2.html#V1" title="ORDINAL2:attr.1">Ordinal-yielding</a> </span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">take </span>
<font color="Maroon" title="c3">a</font>
; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="ordinal2.html#D8" title="ORDINAL2:def.8">ORDINAL2:def 8</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Maroon" title="c1">S1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">a</font></span><br/>

<a NAME="E1:7_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">S1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c2">S2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal5.html#T3" target="_self" title="ORDINAL5:th.3">ThS1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:7_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Maroon" title="c1">S1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:7"><span class="lab"><font color="Green" title="E5">A0</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</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/>


</div><span class="kw">end;</span></div>

<span class="kw">take </span>
<font color="Maroon" title="c3">a</font>
; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="ordinal2.html#D8" title="ORDINAL2:def.8">ORDINAL2:def 8</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Maroon" title="c2">S2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">a</font></span><br/>

<a NAME="E4:7"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">S2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <font color="Maroon" title="c2">S2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal5.html#T3" target="_self" title="ORDINAL5:th.3">ThS1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:7"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <font color="Maroon" title="c2">S2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:7"><span class="lab"><font color="Green" title="E5">A0</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</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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