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<span class="kw">set </span><font color="Maroon" title="c4">R</font> = <font color="Maroon" title="c2">R1</font> <a href="proofs_1.html#K5" title="PROOFS_1:func.5">\/</a> <font color="Maroon" title="c3">R2</font>;<br/>
<a NAME="E1:13_1_1"/><span class="lab"><font color="Green" title="E6">A1</font></span>: 
(  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">R1</font> <a href="proofs_1.html#K5" title="PROOFS_1:func.5">\/</a> <font color="Maroon" title="c3">R2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c2">R1</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#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c3">R2</font></span>)</span> &amp;  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c2">R1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <font color="Maroon" title="c1">Fml</font> &amp;  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c3">R2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="finsub_1.html#K5" title="FINSUB_1:func.5">Fin</a> <font color="Maroon" title="c1">Fml</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="proofs_1.html#D2" target="_self" onmouseover="rs('proofs_1/D2')" onmouseout="rh()">Def2</a>, <a class="ref" href="xtuple_0.html#T23" onmouseover="rs('xtuple_0/T23')" onmouseout="rh()">XTUPLE_0:23</a></span>;<br/>
<a NAME="E2:13_1_1"/>
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">R1</font> <a href="proofs_1.html#K5" title="PROOFS_1:func.5">\/</a> <font color="Maroon" title="c3">R2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">rng</a> <font color="Maroon" title="c2">R1</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#NK2" title="RELAT_1:NK.2">rng</a> <font color="Maroon" title="c3">R2</font></span>)</span> &amp;  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">rng</a> <font color="Maroon" title="c2">R1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">Fml</font> &amp;  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">rng</a> <font color="Maroon" title="c3">R2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">Fml</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="proofs_1.html#D2" target="_self" onmouseover="rs('proofs_1/D2')" onmouseout="rh()">Def2</a>, <a class="ref" href="relat_1.html#T12" onmouseover="rs('relat_1/T12')" onmouseout="rh()">RELAT_1:12</a></span>;<br/>
<a NAME="E3:13_1_1"/><span class="kw">then </span>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">R1</font> <a href="proofs_1.html#K5" title="PROOFS_1:func.5">\/</a> <font color="Maroon" title="c3">R2</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">Fml</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T8" onmouseover="rs('xboole_1/T8')" onmouseout="rh()">XBOOLE_1:8</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:13_1_1"/>
<font color="Maroon" title="c2">R1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c3">R2</font> is    <a href="proofs_1.html#M1" title="PROOFS_1:mode.1">Rule</a> of <font color="Maroon" title="c1">Fml</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_1_1"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="ref" href="proofs_1.html#D2" target="_self" onmouseover="rs('proofs_1/D2')" onmouseout="rh()">Def2</a>, <a class="ref" href="xboole_1.html#T8" onmouseover="rs('xboole_1/T8')" onmouseout="rh()">XBOOLE_1:8</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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