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<b>let </b><font color="Maroon" title="c1">f1</font>, <font color="Maroon" title="c2">f2</font> be   <a href="ordinal2.html#NM1" title="ORDINAL2:NM.1">Ordinal-Sequence</a>;<br/>



<b>assume </b><a NAME="E1:15"/><i><font color="Green" title="E14">A1</font></i>: 
<font color="Maroon" title="c1">f1</font> is <a href="ordinal2.html#V2" title="ORDINAL2:attr.2">increasing</a>
 ;<br/>

<a NAME="E2:15"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c1">f1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">f1</font> <a href="relat_1.html#K10" title="RELAT_1:func.10">"</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">f2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T182" title="RELAT_1:th.182">RELAT_1:182</a></i>;<br/>
<a NAME="E3:15"/><b>then </b>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c1">f1</font></span>)</span> is   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>
 
<b>by </b><i><a class="txt" href="ordinal4.html#E1:15"><i><font color="Green" title="E14">A1</font></i></a>, <a class="ref" href="ordinal4.html#T11" target="_self" title="ORDINAL4:th.11">Th11</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c3">f</font> = <font color="Maroon" title="c2">f2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c1">f1</font> as   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">T-Sequence</a> <b>by </b><i><a class="ref" href="ordinal1.html#D7" title="ORDINAL1:def.7">ORDINAL1:def 7</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c4">A</font> being   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a><b> such that </b><br/><a NAME="E6:15"/><i><font color="Green" title="E15">A2</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">f2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">A</font>
 <b>by </b><i><a class="ref" href="ordinal2.html#D8" title="ORDINAL2:def.8">ORDINAL2:def 8</a></i>;<br/>
<a NAME="E7:15"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">f</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> <font color="Maroon" title="c2">f2</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T45" title="RELAT_1:th.45">RELAT_1:45</a></i>;<br/>
<a NAME="E8:15"/><b>then </b>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">A</font>
 
<b>by </b><i><a class="txt" href="ordinal4.html#E6:15"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E9:15"/>
<font color="Maroon" title="c2">f2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c1">f1</font> is   <a href="ordinal2.html#NM1" title="ORDINAL2:NM.1">Ordinal-Sequence</a>
 <b>by </b><i><a class="ref" href="ordinal2.html#D8" title="ORDINAL2:def.8">ORDINAL2:def 8</a></i>;<br/>


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