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<span class="kw">let </span><font color="Maroon" title="c1">A</font> be    <a href="qc_lang1.html#M1" title="QC_LANG1:mode.1">QC-alphabet</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">Y1</font>, <font color="Olive" title="b2">Y2</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="qc_lang1.html#K1" title="QC_LANG1:func.1">QC-symbols</a> <font color="Maroon" title="c1">A</font></span>)</span>  st <font color="Olive" title="b1">Y1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">Y2</font> holds <br/> <a href="qc_lang1.html#K25" title="QC_LANG1:func.25">min</a> <font color="Olive" title="b2">Y2</font> <a href="qc_lang1.html#R1" title="QC_LANG1:pred.1">&lt;=</a>  <a href="qc_lang1.html#K25" title="QC_LANG1:func.25">min</a> <font color="Olive" title="b1">Y1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">Y1</font>, <font color="Maroon" title="c3">Y2</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="qc_lang1.html#K1" title="QC_LANG1:func.1">QC-symbols</a> <font color="Maroon" title="c1">A</font></span>)</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"> ( <font color="Maroon" title="c2">Y1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">Y2</font> implies  <a href="qc_lang1.html#K25" title="QC_LANG1:func.25">min</a> <font color="Maroon" title="c3">Y2</font> <a href="qc_lang1.html#R1" title="QC_LANG1:pred.1">&lt;=</a>  <a href="qc_lang1.html#K25" title="QC_LANG1:func.25">min</a> <font color="Maroon" title="c2">Y1</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:74"/><span class="lab"><font color="Green" title="E47">A1</font></span>: 
<font color="Maroon" title="c2">Y1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">Y2</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">  <a href="qc_lang1.html#K25" title="QC_LANG1:func.25">min</a> <font color="Maroon" title="c3">Y2</font> <a href="qc_lang1.html#R1" title="QC_LANG1:pred.1">&lt;=</a>  <a href="qc_lang1.html#K25" title="QC_LANG1:func.25">min</a> <font color="Maroon" title="c2">Y1</font></span><br/>

<a NAME="E2:74"/>
 <a href="qc_lang1.html#K25" title="QC_LANG1:func.25">min</a> <font color="Maroon" title="c2">Y1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">Y1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#D35" target="_self" onmouseover="rs('qc_lang1/D35')" onmouseout="rh()">Def35</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:74"/>
 <a href="qc_lang1.html#K25" title="QC_LANG1:func.25">min</a> <font color="Maroon" title="c3">Y2</font> <a href="qc_lang1.html#R1" title="QC_LANG1:pred.1">&lt;=</a>  <a href="qc_lang1.html#K25" title="QC_LANG1:func.25">min</a> <font color="Maroon" title="c2">Y1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:74"><span class="lab"><font color="Green" title="E47">A1</font></span></a>, <a class="ref" href="qc_lang1.html#D35" target="_self" onmouseover="rs('qc_lang1/D35')" onmouseout="rh()">Def35</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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