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<b>let </b><font color="Maroon" title="c1">x1</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="binop_1.html#D20" title="BINOP_1:def.20">BINOP_1:def 20</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  holds  <a href="rvsum_1.html#K2" title="RVSUM_1:func.2">sqrreal</a>  <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="binop_2.html#K35" title="BINOP_2:func.35">multreal</a>  <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c1">x1</font>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="binop_2.html#K35" title="BINOP_2:func.35">multreal</a>  <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K2" title="RVSUM_1:func.2">sqrreal</a>  <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c1">x1</font></span>)</span>,<span class="p1">(<span class="default"><a href="rvsum_1.html#K2" title="RVSUM_1:func.2">sqrreal</a>  <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">x2</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <a href="rvsum_1.html#K2" title="RVSUM_1:func.2">sqrreal</a>  <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="binop_2.html#K35" title="BINOP_2:func.35">multreal</a>  <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="binop_2.html#K35" title="BINOP_2:func.35">multreal</a>  <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K2" title="RVSUM_1:func.2">sqrreal</a>  <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c1">x1</font></span>)</span>,<span class="p1">(<span class="default"><a href="rvsum_1.html#K2" title="RVSUM_1:func.2">sqrreal</a>  <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">x2</font></span>)</span></span><br/>



<b>thus </b><a href="rvsum_1.html#K2" title="RVSUM_1:func.2">sqrreal</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><a href="binop_2.html#K35" title="BINOP_2:func.35">multreal</a>  <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c1">x1</font>,<font color="Maroon" title="c2">x2</font></span>)</span> = 
<a href="rvsum_1.html#K2" title="RVSUM_1:func.2">sqrreal</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">x1</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <font color="Maroon" title="c2">x2</font></span>)</span>
<b>by </b><i><a class="ref" href="binop_2.html#D11" title="BINOP_2:def.11">BINOP_2:def 11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">x1</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <font color="Maroon" title="c2">x2</font></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> 
<b>by </b><i><a class="ref" href="rvsum_1.html#D2" target="_self" title="RVSUM_1:def.2">Def2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">x1</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x2</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span>

<br/>.= 
<a href="binop_2.html#K35" title="BINOP_2:func.35">multreal</a>  <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">x1</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">x2</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span>
<b>by </b><i><a class="ref" href="binop_2.html#D11" title="BINOP_2:def.11">BINOP_2:def 11</a></i>
<br/>.= 
<a href="binop_2.html#K35" title="BINOP_2:func.35">multreal</a>  <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K2" title="RVSUM_1:func.2">sqrreal</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">x1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">x2</font> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span>
<b>by </b><i><a class="ref" href="rvsum_1.html#D2" target="_self" title="RVSUM_1:def.2">Def2</a></i>
<br/>.= 
<a href="binop_2.html#K35" title="BINOP_2:func.35">multreal</a>  <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K2" title="RVSUM_1:func.2">sqrreal</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">x1</font></span>)</span>,<span class="p1">(<span class="default"><a href="rvsum_1.html#K2" title="RVSUM_1:func.2">sqrreal</a>  <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">x2</font></span>)</span>
<b>by </b><i><a class="ref" href="rvsum_1.html#D2" target="_self" title="RVSUM_1:def.2">Def2</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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