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<span class="kw">let </span><font color="Maroon" title="c1">M</font> be   <a href="metric_1.html#NM2" title="METRIC_1:NM.2">PseudoMetricSpace</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">x</font>, <font color="Olive" title="b2">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">M</font>  st <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">y</font> <a href="metric_2.html#K1" title="METRIC_2:func.1">-neighbour</a>  holds <br/><font color="Olive" title="b2">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">x</font> <a href="metric_2.html#K1" title="METRIC_2:func.1">-neighbour</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">M</font>; <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">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">y</font> <a href="metric_2.html#K1" title="METRIC_2:func.1">-neighbour</a>  implies <font color="Maroon" title="c3">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">x</font> <a href="metric_2.html#K1" title="METRIC_2:func.1">-neighbour</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:10"/>
<font color="Maroon" title="c2">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">y</font> <a href="metric_2.html#K1" title="METRIC_2:func.1">-neighbour</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="c3">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">x</font> <a href="metric_2.html#K1" title="METRIC_2:func.1">-neighbour</a> </span><br/>

<a NAME="E2:10"/><span class="kw">then </span>
<font color="Maroon" title="c2">x</font> <a href="metric_2.html#R3" title="METRIC_2:pred.3">tolerates</a> <font color="Maroon" title="c3">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="metric_2.html#T2" target="_self" onmouseover="rs('metric_2/T2')" onmouseout="rh()">Th2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:10"/>
<font color="Maroon" title="c3">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">x</font> <a href="metric_2.html#K1" title="METRIC_2:func.1">-neighbour</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"> verum</span><br/>


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