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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">C</font> being non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/> for <font color="Olive" title="b2">V</font> being  <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/> for <font color="Olive" title="b3">f1</font>, <font color="Olive" title="b4">f2</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Olive" title="b1">C</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">V</font>  st <font color="Olive" title="b3">f1</font> <a href="vfunct_1.html#R1" title="VFUNCT_1:pred.1">is_bounded_on</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Olive" title="b4">f2</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">Y</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">V8</a>() holds <br/><font color="Olive" title="b3">f1</font> <a href="vfunct_1.html#K1" title="VFUNCT_1:func.1">+</a> <font color="Olive" title="b4">f2</font> <a href="vfunct_1.html#R1" title="VFUNCT_1:pred.1">is_bounded_on</a> <font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">Y</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">C</font> be  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <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">V</font> being  <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/> for <font color="Olive" title="b2">f1</font>, <font color="Olive" title="b3">f2</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c3">C</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">V</font>  st <font color="Olive" title="b2">f1</font> <a href="vfunct_1.html#R1" title="VFUNCT_1:pred.1">is_bounded_on</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Olive" title="b3">f2</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">Y</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">V8</a>() holds <br/><font color="Olive" title="b2">f1</font> <a href="vfunct_1.html#K1" title="VFUNCT_1:func.1">+</a> <font color="Olive" title="b3">f2</font> <a href="vfunct_1.html#R1" title="VFUNCT_1:pred.1">is_bounded_on</a> <font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">Y</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">V</font> be   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</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">f1</font>, <font color="Olive" title="b2">f2</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c3">C</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">V</font>  st <font color="Olive" title="b1">f1</font> <a href="vfunct_1.html#R1" title="VFUNCT_1:pred.1">is_bounded_on</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Olive" title="b2">f2</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">Y</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">V8</a>() holds <br/><font color="Olive" title="b1">f1</font> <a href="vfunct_1.html#K1" title="VFUNCT_1:func.1">+</a> <font color="Olive" title="b2">f2</font> <a href="vfunct_1.html#R1" title="VFUNCT_1:pred.1">is_bounded_on</a> <font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">Y</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">f1</font>, <font color="Maroon" title="c6">f2</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c3">C</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">V</font>; <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="c5">f1</font> <a href="vfunct_1.html#R1" title="VFUNCT_1:pred.1">is_bounded_on</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c6">f2</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">Y</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">V8</a>() implies <font color="Maroon" title="c5">f1</font> <a href="vfunct_1.html#K1" title="VFUNCT_1:func.1">+</a> <font color="Maroon" title="c6">f2</font> <a href="vfunct_1.html#R1" title="VFUNCT_1:pred.1">is_bounded_on</a> <font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">Y</font> )</span><br/>











<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:69"/><span class="lab"><font color="Green" title="E26">A1</font></span>: 
<font color="Maroon" title="c5">f1</font> <a href="vfunct_1.html#R1" title="VFUNCT_1:pred.1">is_bounded_on</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">and </span><br/><a NAME="E2:69"/><span class="lab"><font color="Green" title="E27">A2</font></span>: 
<font color="Maroon" title="c6">f2</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">Y</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">V8</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="c5">f1</font> <a href="vfunct_1.html#K1" title="VFUNCT_1:func.1">+</a> <font color="Maroon" title="c6">f2</font> <a href="vfunct_1.html#R1" title="VFUNCT_1:pred.1">is_bounded_on</a> <font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">Y</font></span><br/>

<a NAME="E3:69"/>
<font color="Maroon" title="c6">f2</font> <a href="vfunct_1.html#R1" title="VFUNCT_1:pred.1">is_bounded_on</a> <font color="Maroon" title="c2">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:69"><span class="lab"><font color="Green" title="E27">A2</font></span></a>, <a class="ref" href="vfunct_1.html#T61" target="_self" title="VFUNCT_1:th.61">Th61</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:69"/>
<font color="Maroon" title="c5">f1</font> <a href="vfunct_1.html#K1" title="VFUNCT_1:func.1">+</a> <font color="Maroon" title="c6">f2</font> <a href="vfunct_1.html#R1" title="VFUNCT_1:pred.1">is_bounded_on</a> <font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:69"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="ref" href="vfunct_1.html#T53" target="_self" title="VFUNCT_1:th.53">Th53</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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