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<span class="kw">let </span><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">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">E</font> being   <a href="eqrel_1.html#NM1" title="EQREL_1:NM.1">Tolerance</a> of <font color="Maroon" title="c2">X</font> holds <br/> ( <font color="Maroon" title="c1">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="coh_sp.html#K2" title="COH_SP:func.2">CohSp</a> <font color="Olive" title="b1">E</font> iff <font color="Maroon" title="c1">a</font> is    <a href="toler_1.html#M1" title="TOLER_1:mode.1">TolSet</a> of <font color="Olive" title="b1">E</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">E</font> be   <a href="eqrel_1.html#NM1" title="EQREL_1:NM.1">Tolerance</a> of <font color="Maroon" title="c2">X</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="c1">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="coh_sp.html#K2" title="COH_SP:func.2">CohSp</a> <font color="Maroon" title="c3">E</font> iff <font color="Maroon" title="c1">a</font> is    <a href="toler_1.html#M1" title="TOLER_1:mode.1">TolSet</a> of <font color="Maroon" title="c3">E</font> )</span><br/>





<span class="kw">thus </span><a NAME="E1:18"/>
( <font color="Maroon" title="c1">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="coh_sp.html#K2" title="COH_SP:func.2">CohSp</a> <font color="Maroon" title="c3">E</font> implies <font color="Maroon" title="c1">a</font> is    <a href="toler_1.html#M1" title="TOLER_1:mode.1">TolSet</a> of <font color="Maroon" title="c3">E</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="c1">a</font> is    <a href="toler_1.html#M1" title="TOLER_1:mode.1">TolSet</a> of <font color="Maroon" title="c3">E</font> implies <font color="Maroon" title="c1">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="coh_sp.html#K2" title="COH_SP:func.2">CohSp</a> <font color="Maroon" title="c3">E</font> )</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="18_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:18_1"/>
<font color="Maroon" title="c1">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="coh_sp.html#K2" title="COH_SP:func.2">CohSp</a> <font color="Maroon" title="c3">E</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="c1">a</font> is    <a href="toler_1.html#M1" title="TOLER_1:mode.1">TolSet</a> of <font color="Maroon" title="c3">E</font></span><br/>

<a NAME="E2:18_1"/><span class="kw">then </span>
 for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">a</font> &amp; <font color="Olive" title="b2">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">a</font> holds <br/><span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">E</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="coh_sp.html#D3" target="_self" onmouseover="rs('coh_sp/D3')" onmouseout="rh()">Def3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:18_1"/>
<font color="Maroon" title="c1">a</font> is    <a href="toler_1.html#M1" title="TOLER_1:mode.1">TolSet</a> of <font color="Maroon" title="c3">E</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="toler_1.html#D1" onmouseover="rs('toler_1/D1')" onmouseout="rh()">TOLER_1:def 1</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/>


</div><span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E2:18"/>
<font color="Maroon" title="c1">a</font> is    <a href="toler_1.html#M1" title="TOLER_1:mode.1">TolSet</a> of <font color="Maroon" title="c3">E</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="c1">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="coh_sp.html#K2" title="COH_SP:func.2">CohSp</a> <font color="Maroon" title="c3">E</font></span><br/>

<a NAME="E3:18"/><span class="kw">then </span>
 for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">a</font> &amp; <font color="Olive" title="b2">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">a</font> holds <br/><span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">E</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="toler_1.html#D1" onmouseover="rs('toler_1/D1')" onmouseout="rh()">TOLER_1:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:18"/>
<font color="Maroon" title="c1">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="coh_sp.html#K2" title="COH_SP:func.2">CohSp</a> <font color="Maroon" title="c3">E</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="coh_sp.html#D3" target="_self" onmouseover="rs('coh_sp/D3')" onmouseout="rh()">Def3</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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