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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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">  for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  st <font color="Olive" title="b1">f</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b2">g</font> is <font color="Maroon" title="c1">X</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  holds <br/>( <font color="Olive" title="b1">f</font> is <font color="Maroon" title="c1">X</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  &amp; <font color="Olive" title="b2">g</font> is <font color="Maroon" title="c1">X</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">f</font>, <font color="Maroon" title="c3">g</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</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> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">g</font> is <font color="Maroon" title="c1">X</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  implies ( <font color="Maroon" title="c2">f</font> is <font color="Maroon" title="c1">X</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  &amp; <font color="Maroon" title="c3">g</font> is <font color="Maroon" title="c1">X</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  ) )</span><br/>



<span class="kw">set </span><font color="Maroon" title="c4">h</font> = <font color="Maroon" title="c2">f</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">g</font>;<br/>
<span class="kw">assume </span><a NAME="E1:5"/>
<font color="Maroon" title="c2">f</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">g</font> is <font color="Maroon" title="c1">X</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</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 <font color="Maroon" title="c1">X</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  &amp; <font color="Maroon" title="c3">g</font> is <font color="Maroon" title="c1">X</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  )</span><br/>

<a NAME="E2:5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E18">A1</font></span>: 
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D19" onmouseover="rs('relat_1/D19')" onmouseout="rh()">RELAT_1:def 19</a></span>;<br/>
<a NAME="E3:5"/>
(  <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>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">g</font></span>)</span> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c3">g</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">g</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T29" onmouseover="rs('finseq_1/T29')" onmouseout="rh()">FINSEQ_1:29</a>, <a class="ref" href="finseq_1.html#T30" onmouseover="rs('finseq_1/T30')" onmouseout="rh()">FINSEQ_1:30</a></span>;<br/>
<a NAME="E4:5"/><span class="kw">then </span>
(  <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> <font color="Maroon" title="c1">X</font> &amp;  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c3">g</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:5"><span class="lab"><font color="Green" title="E18">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:5"/>
( <font color="Maroon" title="c2">f</font> is <font color="Maroon" title="c1">X</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  &amp; <font color="Maroon" title="c3">g</font> is <font color="Maroon" title="c1">X</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D19" onmouseover="rs('relat_1/D19')" onmouseout="rh()">RELAT_1:def 19</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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