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<span class="kw">consider </span><font color="Maroon" title="c1">S</font> being    <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</a> ;<br/>
<span class="kw">take </span><font color="Maroon" title="c2">f</font> = <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( not <font color="Maroon" title="c2">f</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp; <font color="Maroon" title="c2">f</font> is  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>  &amp; <font color="Maroon" title="c2">f</font> is  <a href="pralg_1.html#V2" title="PRALG_1:attr.2">1-sorted-yielding</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E2:13_1_1"/>
not <font color="Maroon" title="c2">f</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</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">f</font> is  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>  &amp; <font color="Maroon" title="c2">f</font> is  <a href="pralg_1.html#V2" title="PRALG_1:attr.2">1-sorted-yielding</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E3:13_1_1"/>
<font color="Maroon" title="c2">f</font> is  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</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">f</font> is  <a href="pralg_1.html#V2" title="PRALG_1:attr.2">1-sorted-yielding</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="pralg_1.html#D11" title="PRALG_1:def.11">PRALG_1:def 11</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <font color="Maroon" title="c2">f</font> or <font color="Maroon" title="c2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> is    <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E4:13_1_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c2">f</font>
 ; <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">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> is    <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</a> </span><br/>

<span class="kw">hence </span><a NAME="E5:13_1_1"/>
<font color="Maroon" title="c2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> is    <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</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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