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<b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">b</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">n</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">M1</font> be   <a href="matrix_1.html#NM3">Matrix</a> of <font color="Maroon">n</font>, <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">M2</font> be   <a href="matrix_1.html#NM3">Matrix</a> of <font color="Maroon">n</font>, <a href="numbers.html#K1">REAL</a> ;<br/>









<b>assume </b><a NAME="E1:59"/>
( <font color="Maroon">a</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <font color="Maroon">b</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <font color="Maroon">M1</font> is <a href="matrix10.html#V4" target="_self">Nonnegative</a> &amp; <font color="Maroon">M2</font> is <a href="matrix10.html#V4" target="_self">Nonnegative</a> )
 ;<br/>

<a NAME="E2:59"/><b>then </b>
( <font color="Maroon">a</font> <a href="matrix10.html#K5" target="_self">*</a> <font color="Maroon">M1</font> is <a href="matrix10.html#V4" target="_self">Nonnegative</a> &amp; <font color="Maroon">b</font> <a href="matrix10.html#K5" target="_self">*</a> <font color="Maroon">M2</font> is <a href="matrix10.html#V4" target="_self">Nonnegative</a> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:59"/>
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="matrix10.html#K5" target="_self">*</a> <font color="Maroon">M1</font></span>)</span> <a href="matrix10.html#K3" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="matrix10.html#K5" target="_self">*</a> <font color="Maroon">M2</font></span>)</span> is <a href="matrix10.html#V4" target="_self">Nonnegative</a>
 <b>by </b><i/>;<br/>


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