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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="bhsp_1.html#NM1">RealUnitarySpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be  <a href="bhsp_1.html#V1">strict</a>  <a href="rusub_1.html#M1">Subspace</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="lattices.html#G3">LattStr</a>(# <span class="p1">(<span class="default"><a href="rusub_2.html#K3" target="_self">Subspaces</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="rusub_2.html#K5" target="_self">SubJoin</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="rusub_2.html#K6" target="_self">SubMeet</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> #);<br/>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="rusub_2.html#K2" target="_self">/\</a> <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="rusub_2.html#K2" target="_self">/\</a> <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <a href="lattices.html#G3">LattStr</a>(# <span class="p1">(<span class="default"><a href="rusub_2.html#K3" target="_self">Subspaces</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="rusub_2.html#K5" target="_self">SubJoin</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="rusub_2.html#K6" target="_self">SubMeet</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> #) <b>by </b><i><a class="ref" href="rusub_2.html#D3" target="_self">Def3</a></i>;<br/>
<b>assume </b><a NAME="E2:83"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is    <a href="rusub_1.html#M1">Subspace</a> of <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">c<sub>7</sub></font> = 
<span class="p1">(<span class="default"><a href="rusub_2.html#K5" target="_self">SubJoin</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="lattices.html#D1">LATTICES:def 1</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="rusub_2.html#K1" target="_self">+</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="rusub_2.html#D7" target="_self">Def7</a></i>
<br/>.= 
<font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="rusub_2.html#E2:83"><i><font color="Green">E60</font></i></a>, <a class="ref" href="rusub_2.html#T8" target="_self">Th8</a></i>
;<br/>
<a NAME="E4:83"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="ref" href="lattices.html#D3">LATTICES:def 3</a></i>;<br/>
<a NAME="E5:83"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>8</sub></font> <a href="lattices.html#R3">[=</a> <font color="Maroon">c<sub>7</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="ref" href="lattices.html#T27">LATTICES:27</a></i>;<br/>
<a NAME="E6:83"/><b>then </b><i><font color="Green">E61</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="ref" href="lattices.html#D3">LATTICES:def 3</a></i>;<br/>
<i><font color="Green">E62</font></i>: <font color="Maroon">c<sub>7</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>8</sub></font> = 
<span class="p1">(<span class="default"><a href="rusub_2.html#K6" target="_self">SubMeet</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="ref" href="lattices.html#D2">LATTICES:def 2</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="rusub_2.html#K2" target="_self">/\</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="rusub_2.html#D8" target="_self">Def8</a></i>
;<br/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="rusub_2.html#K5" target="_self">SubJoin</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D1">LATTICES:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rusub_2.html#K5" target="_self">SubJoin</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rusub_2.html#K6" target="_self">SubMeet</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D2">LATTICES:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rusub_2.html#K5" target="_self">SubJoin</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rusub_2.html#K6" target="_self">SubMeet</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rusub_2.html#K6" target="_self">SubMeet</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="lattices.html#D2">LATTICES:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rusub_2.html#K5" target="_self">SubJoin</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rusub_2.html#K6" target="_self">SubMeet</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font></span>)</span>,<font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="ref" href="rusub_2.html#D8" target="_self">Def8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rusub_2.html#K5" target="_self">SubJoin</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="ref" href="rusub_2.html#D8" target="_self">Def8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rusub_2.html#K2" target="_self">/\</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="rusub_2.html#K1" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rusub_2.html#K2" target="_self">/\</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="rusub_2.html#D7" target="_self">Def7</a></i>
;<br/>
<b>hence </b><a NAME="E9:83"/>
<font color="Maroon">c<sub>2</sub></font> <a href="rusub_2.html#K2" target="_self">/\</a> <font color="Maroon">c<sub>4</sub></font> is    <a href="rusub_1.html#M1">Subspace</a> of <font color="Maroon">c<sub>3</sub></font> <a href="rusub_2.html#K2" target="_self">/\</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="rusub_2.html#E6:83"><i><font color="Green">E61</font></i></a>, <a class="txt" href="rusub_2.html#E7:83"><i><font color="Green">E62</font></i></a>, <a class="ref" href="rusub_2.html#T8" target="_self">Th8</a></i>;<br/>


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