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<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="82_1_1_1"><span class="kw">now </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">  for <font color="Olive" title="b1">x</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>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="mesfunc1.html#K7" title="MESFUNC1:func.7">-</a> <font color="Maroon" title="c2">f</font></span>)</span> holds <br/> <a href="xxreal_0.html#K2" title="XXREAL_0:func.2">-infty</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="mesfunc1.html#K7" title="MESFUNC1:func.7">-</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Olive" title="b1">x</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c3">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"> ( <font color="Maroon" title="c3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="mesfunc1.html#K7" title="MESFUNC1:func.7">-</a> <font color="Maroon" title="c2">f</font></span>)</span> implies  <a href="xxreal_0.html#K2" title="XXREAL_0:func.2">-infty</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="mesfunc1.html#K7" title="MESFUNC1:func.7">-</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font> )</span><br/><span class="kw">assume </span><a NAME="E1:82_1_1_1"/><span class="lab"><font color="Green" title="E58">A1</font></span>: 
<font color="Maroon" title="c3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="mesfunc1.html#K7" title="MESFUNC1:func.7">-</a> <font color="Maroon" title="c2">f</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">  <a href="xxreal_0.html#K2" title="XXREAL_0:func.2">-infty</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="mesfunc1.html#K7" title="MESFUNC1:func.7">-</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font></span><br/><a NAME="E2:82_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c2">f</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="mesfunc1.html#D7" onmouseover="rs('mesfunc1/D7')" onmouseout="rh()">MESFUNC1:def 7</a></span>;<br/><a NAME="E3:82_1_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</a> 1</span>)</span> <a href="xxreal_3.html#K4" title="XXREAL_3:func.4">*</a> <a href="xxreal_0.html#K1" title="XXREAL_0:func.1">+infty</a> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</a> 1</span>)</span> <a href="xxreal_3.html#K4" title="XXREAL_3:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="mesfunc5.html#T11" onmouseover="rs('mesfunc5/T11')" onmouseout="rh()">MESFUNC5:11</a>, <a class="ref" href="xxreal_3.html#T102" onmouseover="rs('xxreal_3/T102')" onmouseout="rh()">XXREAL_3:102</a></span>;<br/><a NAME="E4:82_1_1_1"/><span class="kw">then </span>
 <a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</a> <a href="xxreal_0.html#K1" title="XXREAL_0:func.1">+infty</a> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</a> 1</span>)</span> <a href="xxreal_3.html#K4" title="XXREAL_3:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_3.html#T91" onmouseover="rs('xxreal_3/T91')" onmouseout="rh()">XXREAL_3:91</a></span>;<br/><a NAME="E5:82_1_1_1"/><span class="kw">then </span>
 <a href="xxreal_0.html#K2" title="XXREAL_0:func.2">-infty</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="xxreal_3.html#K7" title="XXREAL_3:func.7">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_3.html#T6" onmouseover="rs('xxreal_3/T6')" onmouseout="rh()">XXREAL_3:6</a>, <a class="ref" href="xxreal_3.html#T91" onmouseover="rs('xxreal_3/T91')" onmouseout="rh()">XXREAL_3:91</a></span>;<br/><span class="kw">hence </span><a NAME="E6:82_1_1_1"/>
 <a href="xxreal_0.html#K2" title="XXREAL_0:func.2">-infty</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="mesfunc1.html#K7" title="MESFUNC1:func.7">-</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="supinf_2.html#K9" title="SUPINF_2:func.9">.</a> <font color="Maroon" title="c3">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:82_1_1_1"><span class="lab"><font color="Green" title="E58">A1</font></span></a>, <a class="ref" href="mesfunc1.html#D7" onmouseover="rs('mesfunc1/D7')" onmouseout="rh()">MESFUNC1:def 7</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">hence </span><a NAME="E2:82_1_1"/>
 <a href="mesfunc1.html#K7" title="MESFUNC1:func.7">-</a> <font color="Maroon" title="c2">f</font> is <a href="mesfunc5.html#V3" title="MESFUNC5:attr.3">V178</a>()
 <span class="kw">by</span> <span class="lab"><a class="ref" href="mesfunc5.html#T10" onmouseover="rs('mesfunc5/T10')" onmouseout="rh()">MESFUNC5:10</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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