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<span class="kw">let </span><font color="Maroon" title="c4">F</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</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">S</font> being  <a href="symsp_1.html#NM1" title="SYMSP_1:NM.1">SymSp</a> of <font color="Maroon" title="c4">F</font><br/> for <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">S</font>  st not <font color="Olive" title="b3">a</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp; not <font color="Olive" title="b3">a</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  holds <br/> <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Olive" title="b3">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">c</font>,<font color="Olive" title="b2">b</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c5">S</font> be   <a href="symsp_1.html#NM1" title="SYMSP_1:NM.1">SymSp</a> of <font color="Maroon" title="c4">F</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">b</font>, <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">S</font>  st not <font color="Olive" title="b2">a</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp; not <font color="Olive" title="b2">a</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  holds <br/> <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b1">b</font>,<font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">c</font>,<font color="Olive" title="b1">b</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c6">b</font>, <font color="Maroon" title="c7">a</font>, <font color="Maroon" title="c8">c</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( not <font color="Maroon" title="c7">a</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  &amp; not <font color="Maroon" title="c7">a</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a>  implies  <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">b</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a>  )</span><br/>









<span class="kw">set </span><font color="Maroon" title="c9">1F</font> =  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c4">F</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">0F</font> =  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">F</font>;<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:51"/><span class="lab"><font color="Green" title="E32">A1</font></span>: 
not <font color="Maroon" title="c7">a</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a> 
 <span class="kw">and </span><br/><a NAME="E2:51"/><span class="lab"><font color="Green" title="E33">A2</font></span>: 
not <font color="Maroon" title="c7">a</font> <a href="symsp_1.html#NR1" title="SYMSP_1:NR.1">_|_</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">b</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span><br/>

<a NAME="E3:51"/><span class="lab"><font color="Green" title="E34">A3</font></span>: 
 <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:51"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="txt" href="#E2:51"><span class="lab"><font color="Green" title="E33">A2</font></span></a>, <a class="ref" href="symsp_1.html#T36" target="_self" title="SYMSP_1:th.36">Th36</a></span>;<br/>
<a NAME="E4:51"/>
<span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c6">b</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">c</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:51"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="txt" href="#E2:51"><span class="lab"><font color="Green" title="E33">A2</font></span></a>, <a class="ref" href="symsp_1.html#T37" target="_self" title="SYMSP_1:th.37">Th37</a></span>;<br/>
<a NAME="E5:51"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">c</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:51"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="ref" href="symsp_1.html#T35" target="_self" title="SYMSP_1:th.35">Th35</a></span>;<br/>
<a NAME="E6:51"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A4</font></span>: 
<span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">c</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#D19" title="VECTSP_1:def.19">VECTSP_1:def 19</a></span>;<br/>
<a NAME="E7:51"/>
 <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:51"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="txt" href="#E2:51"><span class="lab"><font color="Green" title="E33">A2</font></span></a>, <a class="ref" href="symsp_1.html#T36" target="_self" title="SYMSP_1:th.36">Th36</a></span>;<br/>
<a NAME="E8:51"/><span class="kw">then </span>
 <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c4">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">b</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">c</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:51"><span class="lab"><font color="Green" title="E35">A4</font></span></a>, <a class="ref" href="vectsp_1.html#D22" title="VECTSP_1:def.22">VECTSP_1:def 22</a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">b</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">b</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">b</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">c</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#D19" title="VECTSP_1:def.19">VECTSP_1:def 19</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">b</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">b</font></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">c</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">c</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c4">F</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:51"><span class="lab"><font color="Green" title="E34">A3</font></span></a>, <a class="ref" href="vectsp_1.html#D22" title="VECTSP_1:def.22">VECTSP_1:def 22</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E10:51"/>
 <a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c8">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" title="SYMSP_1:func.1">ProJ</a> <font color="Maroon" title="c7">a</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">b</font></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#D19" title="VECTSP_1:def.19">VECTSP_1:def 19</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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