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<b>let </b><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</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> ;<br/><b>let </b><font color="Maroon" title="c3">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>let </b><font color="Maroon" title="c4">M1</font>, <font color="Maroon" title="c5">M2</font> be   <a href="matrix_1.html#NM3" title="MATRIX_1:NM.3">Matrix</a> of <font color="Maroon" title="c3">n</font>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/>









<b>assume </b><a NAME="E1:58"/>
( <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c2">b</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c4">M1</font> is <a href="matrix10.html#V4" title="MATRIX10:attr.4">Nonnegative</a> &amp; <font color="Maroon" title="c5">M2</font> is <a href="matrix10.html#V4" title="MATRIX10:attr.4">Nonnegative</a> )
 ;<br/>

<a NAME="E2:58"/><b>then </b>
( <font color="Maroon" title="c1">a</font> <a href="matrix10.html#K5" title="MATRIX10:func.5">*</a> <font color="Maroon" title="c4">M1</font> is <a href="matrix10.html#V4" title="MATRIX10:attr.4">Nonnegative</a> &amp; <font color="Maroon" title="c2">b</font> <a href="matrix10.html#K5" title="MATRIX10:func.5">*</a> <font color="Maroon" title="c5">M2</font> is <a href="matrix10.html#V4" title="MATRIX10:attr.4">Nonnegative</a> )
 
<b>by </b><i><a class="ref" href="matrix10.html#T42" target="_self" title="MATRIX10:th.42">Th42</a></i>;<br/>
<b>hence </b><a NAME="E3:58"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="matrix10.html#K5" title="MATRIX10:func.5">*</a> <font color="Maroon" title="c4">M1</font></span>)</span> <a href="matrix10.html#K3" title="MATRIX10:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">b</font> <a href="matrix10.html#K5" title="MATRIX10:func.5">*</a> <font color="Maroon" title="c5">M2</font></span>)</span> is <a href="matrix10.html#V4" title="MATRIX10:attr.4">Nonnegative</a>
 <b>by </b><i><a class="ref" href="matrix10.html#T36" target="_self" title="MATRIX10:th.36">Th36</a></i>;<br/>


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