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<span class="kw">let </span><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">f</font> being  <a href="valued_0.html#V3" title="VALUED_0:attr.3">real-valued</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b1">f</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font> is  <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a>  &amp; <font color="Olive" title="b1">f</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c2">Y</font> is  <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a>  holds <br/><font color="Olive" title="b1">f</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">Y</font></span>)</span> is  <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">f</font> be   <a href="valued_0.html#V3" title="VALUED_0:attr.3">real-valued</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</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="c3">f</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font> is  <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a>  &amp; <font color="Maroon" title="c3">f</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c2">Y</font> is  <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a>  implies <font color="Maroon" title="c3">f</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">Y</font></span>)</span> is  <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a>  )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:119"/><span class="lab"><font color="Green" title="E48">A1</font></span>: 
<font color="Maroon" title="c3">f</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c1">X</font> is  <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> 
 <span class="kw">and </span><br/><a NAME="E2:119"/><span class="lab"><font color="Green" title="E49">A2</font></span>: 
<font color="Maroon" title="c3">f</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c2">Y</font> is  <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</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="c3">f</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">Y</font></span>)</span> is  <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> </span><br/>

<span class="kw">thus </span><a NAME="E3:119"/>
<font color="Maroon" title="c3">f</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">Y</font></span>)</span> is  <a href="seq_2.html#V1" title="SEQ_2:attr.1">bounded_above</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:119"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="txt" href="#E2:119"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="ref" href="rfunct_1.html#T102" target="_self" title="RFUNCT_1:th.102">Th102</a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="seq_2.html#D8" title="SEQ_2:def.8">SEQ_2:def 8</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="c3">f</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">Y</font></span>)</span> is  <a href="seq_2.html#V2" title="SEQ_2:attr.2">bounded_below</a> </span><br/>

<span class="kw">thus </span><a NAME="E4:119"/>
<font color="Maroon" title="c3">f</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">Y</font></span>)</span> is  <a href="seq_2.html#V2" title="SEQ_2:attr.2">bounded_below</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:119"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="txt" href="#E2:119"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="ref" href="rfunct_1.html#T103" target="_self" title="RFUNCT_1:th.103">Th103</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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