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<b>let </b><font color="Maroon" title="c1">w1</font>, <font color="Maroon" title="c2">w2</font> be   <a href="supinf_1.html#NM3" title="SUPINF_1:NM.3">R_eal</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">wr1</font>, <font color="Olive" title="b2">wr2</font>, <font color="Olive" title="b3">p1</font>, <font color="Olive" title="b4">p2</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Maroon" title="c1">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">wr1</font> &amp; <font color="Maroon" title="c2">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">wr2</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b3">p1</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <font color="Olive" title="b1">wr1</font></span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">p2</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <font color="Olive" title="b2">wr2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Olive" title="b3">p1</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <font color="Maroon" title="c1">w1</font></span>)</span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Olive" title="b4">p2</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <font color="Maroon" title="c2">w2</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">wr1</font>, <font color="Maroon" title="c4">wr2</font>, <font color="Maroon" title="c5">p1</font>, <font color="Maroon" title="c6">p2</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">wr1</font> &amp; <font color="Maroon" title="c2">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">wr2</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c5">p1</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <font color="Maroon" title="c3">wr1</font></span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">p2</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <font color="Maroon" title="c4">wr2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c5">p1</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <font color="Maroon" title="c1">w1</font></span>)</span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c6">p2</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <font color="Maroon" title="c2">w2</font></span>)</span> )</span><br/>



<b>assume </b><a NAME="E1:36"/>
( <font color="Maroon" title="c1">w1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">wr1</font> &amp; <font color="Maroon" title="c2">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">wr2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c5">p1</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <font color="Maroon" title="c3">wr1</font></span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">p2</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <font color="Maroon" title="c4">wr2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c5">p1</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <font color="Maroon" title="c1">w1</font></span>)</span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c6">p2</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <font color="Maroon" title="c2">w2</font></span>)</span></span><br/>

<a NAME="E2:36"/><b>then </b>
( <font color="Maroon" title="c5">p1</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <font color="Maroon" title="c3">wr1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c5">p1</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <font color="Maroon" title="c1">w1</font> &amp; <font color="Maroon" title="c6">p2</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <font color="Maroon" title="c4">wr2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c6">p2</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <font color="Maroon" title="c2">w2</font> )
 
<b>by </b><i><a class="txt" href="convfun1.html#E30"><i><font color="Green" title="E26">Lm15</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:36"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">p1</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <font color="Maroon" title="c3">wr1</font></span>)</span> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">p2</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <font color="Maroon" title="c4">wr2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c5">p1</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <font color="Maroon" title="c1">w1</font></span>)</span> <a href="supinf_2.html#K2" title="SUPINF_2:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="measure6.html#K1" title="MEASURE6:func.1">R_EAL</a> <font color="Maroon" title="c6">p2</font></span>)</span> <a href="extreal1.html#K1" title="EXTREAL1:func.1">*</a> <font color="Maroon" title="c2">w2</font></span>)</span>
 <b>by </b><i><a class="ref" href="supinf_2.html#T1" title="SUPINF_2:th.1">SUPINF_2:1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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