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<span class="kw">let </span><font color="Maroon" title="c1">Y</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">Y0</font> being non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="tsp_1.html#M2" title="TSP_1:mode.2">SubSpace</a> of <font color="Maroon" title="c1">Y</font><br/> for <font color="Olive" title="b2">Y1</font> being non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#V6" title="PRE_TOPC:attr.6">V130</a>()  <a href="tsp_1.html#M2" title="TSP_1:mode.2">SubSpace</a> of <font color="Maroon" title="c1">Y</font>  st <font color="Olive" title="b1">Y0</font> is    <a href="tsp_1.html#M2" title="TSP_1:mode.2">SubSpace</a> of <font color="Olive" title="b2">Y1</font> holds <br/><font color="Olive" title="b1">Y0</font> is  <a href="pre_topc.html#V6" title="PRE_TOPC:attr.6">T_0</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">Y0</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="tsp_1.html#M2" title="TSP_1:mode.2">SubSpace</a> of <font color="Maroon" title="c1">Y</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">Y1</font> being non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#V6" title="PRE_TOPC:attr.6">V130</a>()  <a href="tsp_1.html#M2" title="TSP_1:mode.2">SubSpace</a> of <font color="Maroon" title="c1">Y</font>  st <font color="Maroon" title="c2">Y0</font> is    <a href="tsp_1.html#M2" title="TSP_1:mode.2">SubSpace</a> of <font color="Olive" title="b1">Y1</font> holds <br/><font color="Maroon" title="c2">Y0</font> is  <a href="pre_topc.html#V6" title="PRE_TOPC:attr.6">T_0</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">Y1</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#V6" title="PRE_TOPC:attr.6">V130</a>()  <a href="tsp_1.html#M2" title="TSP_1:mode.2">SubSpace</a> of <font color="Maroon" title="c1">Y</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">Y0</font> is    <a href="tsp_1.html#M2" title="TSP_1:mode.2">SubSpace</a> of <font color="Maroon" title="c3">Y1</font> implies <font color="Maroon" title="c2">Y0</font> is  <a href="pre_topc.html#V6" title="PRE_TOPC:attr.6">T_0</a>  )</span><br/>





<span class="kw">reconsider </span><font color="Maroon" title="c4">A1</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">Y1</font>, <font color="Maroon" title="c5">A0</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">Y0</font> as  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">Y</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="tsp_1.html#E29"><span class="lab"><font color="Green" title="E22">Lm3</font></span></a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:39"/><span class="lab"><font color="Green" title="E25">A1</font></span>: 
<font color="Maroon" title="c2">Y0</font> is    <a href="tsp_1.html#M2" title="TSP_1:mode.2">SubSpace</a> of <font color="Maroon" title="c3">Y1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">Y0</font> is  <a href="pre_topc.html#V6" title="PRE_TOPC:attr.6">T_0</a> </span><br/>

<a NAME="E3:39"/><span class="lab"><font color="Green" title="E26">A2</font></span>: 
<font color="Maroon" title="c4">A1</font> is  <a href="tsp_1.html#V1" title="TSP_1:attr.1">T_0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tsp_1.html#T15" target="_self" title="TSP_1:th.15">Th15</a></span>;<br/>
<a NAME="E4:39"/>
(  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">Y0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">A0</font> &amp;  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c3">Y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">A1</font> )
 
;<br/>
<a NAME="E5:39"/><span class="kw">then </span>
<font color="Maroon" title="c5">A0</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">A1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:39"><span class="lab"><font color="Green" title="E25">A1</font></span></a>, <a class="ref" href="pre_topc.html#D9" title="PRE_TOPC:def.9">PRE_TOPC:def 9</a></span>;<br/>
<a NAME="E6:39"/><span class="kw">then </span>
<font color="Maroon" title="c5">A0</font> is  <a href="tsp_1.html#V1" title="TSP_1:attr.1">T_0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:39"><span class="lab"><font color="Green" title="E26">A2</font></span></a>, <a class="ref" href="tsp_1.html#T7" target="_self" title="TSP_1:th.7">Th7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:39"/>
<font color="Maroon" title="c2">Y0</font> is  <a href="pre_topc.html#V6" title="PRE_TOPC:attr.6">T_0</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tsp_1.html#T15" target="_self" title="TSP_1:th.15">Th15</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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