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<span class="kw">let </span><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</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">X1</font>, <font color="Olive" title="b2">X2</font>, <font color="Olive" title="b3">X3</font> being non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b4">f1</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">X1</font>,<font color="Maroon" title="c2">Y</font><br/> for <font color="Olive" title="b5">f2</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b2">X2</font>,<font color="Maroon" title="c2">Y</font><br/> for <font color="Olive" title="b6">f3</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b3">X3</font>,<font color="Maroon" title="c2">Y</font>  st ( <font color="Olive" title="b1">X1</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</a> <font color="Olive" title="b2">X2</font> or <font color="Olive" title="b4">f1</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Olive" title="b2">X2</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b5">f2</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Olive" title="b2">X2</font></span>)</span> ) &amp; ( <font color="Olive" title="b1">X1</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</a> <font color="Olive" title="b3">X3</font> or <font color="Olive" title="b4">f1</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Olive" title="b3">X3</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b6">f3</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Olive" title="b3">X3</font></span>)</span> ) &amp; ( <font color="Olive" title="b2">X2</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</a> <font color="Olive" title="b3">X3</font> or <font color="Olive" title="b5">f2</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Olive" title="b3">X3</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b6">f3</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Olive" title="b3">X3</font></span>)</span> ) holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b4">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Olive" title="b5">f2</font></span>)</span> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Olive" title="b6">f3</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b4">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">f2</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Olive" title="b6">f3</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">X1</font>, <font color="Maroon" title="c4">X2</font>, <font color="Maroon" title="c5">X3</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</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">f1</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c3">X1</font>,<font color="Maroon" title="c2">Y</font><br/> for <font color="Olive" title="b2">f2</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c4">X2</font>,<font color="Maroon" title="c2">Y</font><br/> for <font color="Olive" title="b3">f3</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c5">X3</font>,<font color="Maroon" title="c2">Y</font>  st ( <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</a> <font color="Maroon" title="c4">X2</font> or <font color="Olive" title="b1">f1</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b2">f2</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c4">X2</font></span>)</span> ) &amp; ( <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</a> <font color="Maroon" title="c5">X3</font> or <font color="Olive" title="b1">f1</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b3">f3</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> ) &amp; ( <font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</a> <font color="Maroon" title="c5">X3</font> or <font color="Olive" title="b2">f2</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b3">f3</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> ) holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b1">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Olive" title="b2">f2</font></span>)</span> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Olive" title="b3">f3</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b1">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">f2</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Olive" title="b3">f3</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c6">f1</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c3">X1</font>,<font color="Maroon" title="c2">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">f2</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c4">X2</font>,<font color="Maroon" title="c2">Y</font><br/> for <font color="Olive" title="b2">f3</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c5">X3</font>,<font color="Maroon" title="c2">Y</font>  st ( <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</a> <font color="Maroon" title="c4">X2</font> or <font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">f2</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c4">X2</font></span>)</span> ) &amp; ( <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</a> <font color="Maroon" title="c5">X3</font> or <font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b2">f3</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> ) &amp; ( <font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</a> <font color="Maroon" title="c5">X3</font> or <font color="Olive" title="b1">f2</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b2">f3</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> ) holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Olive" title="b1">f2</font></span>)</span> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Olive" title="b2">f3</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f2</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Olive" title="b2">f3</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c7">f2</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c4">X2</font>,<font color="Maroon" title="c2">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">f3</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c5">X3</font>,<font color="Maroon" title="c2">Y</font>  st ( <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</a> <font color="Maroon" title="c4">X2</font> or <font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c7">f2</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c4">X2</font></span>)</span> ) &amp; ( <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</a> <font color="Maroon" title="c5">X3</font> or <font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">f3</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> ) &amp; ( <font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</a> <font color="Maroon" title="c5">X3</font> or <font color="Maroon" title="c7">f2</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">f3</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> ) holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Olive" title="b1">f3</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Olive" title="b1">f3</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c8">f3</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c5">X3</font>,<font color="Maroon" title="c2">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="c3">X1</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</a> <font color="Maroon" title="c4">X2</font> or <font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c7">f2</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c4">X2</font></span>)</span> ) &amp; ( <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</a> <font color="Maroon" title="c5">X3</font> or <font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c8">f3</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> ) &amp; ( <font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</a> <font color="Maroon" title="c5">X3</font> or <font color="Maroon" title="c7">f2</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c8">f3</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> ) implies <span class="p1">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c8">f3</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c8">f3</font></span>)</span> )</span><br/>











<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:154"/><span class="lab"><font color="Green" title="E93">A1</font></span>: 
( <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</a> <font color="Maroon" title="c4">X2</font> or <font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c7">f2</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c4">X2</font></span>)</span> )
 <span class="kw">and </span><br/><a NAME="E2:154"/><span class="lab"><font color="Green" title="E94">A2</font></span>: 
( <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</a> <font color="Maroon" title="c5">X3</font> or <font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c8">f3</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> )
 <span class="kw">and </span><br/><a NAME="E3:154"/><span class="lab"><font color="Green" title="E95">A3</font></span>: 
( <font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#R1" title="TSEP_1:pred.1">misses</a> <font color="Maroon" title="c5">X3</font> or <font color="Maroon" title="c7">f2</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c8">f3</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c8">f3</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c8">f3</font></span>)</span></span><br/>

<span class="kw">set </span><font color="Maroon" title="c9">g</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c8">f3</font>;<br/>
<a NAME="E4:154"/><span class="lab"><font color="Green" title="E96">A4</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c5">X3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c5">X3</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tsep_1.html#T21" title="TSEP_1:th.21">TSEP_1:21</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c10">f</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c8">f3</font> as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c5">X3</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">Y</font> ;<br/>
<a NAME="E6:154"/><span class="lab"><font color="Green" title="E97">A5</font></span>: 
<font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c5">X3</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:154"><span class="lab"><font color="Green" title="E96">A4</font></span></a>, <a class="ref" href="tsep_1.html#T22" title="TSEP_1:th.22">TSEP_1:22</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E98">A6</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="154_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:154_1"/><span class="lab"><font color="Green" title="E99">A7</font></span>: 
<font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Maroon" title="c5">X3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c8">f3</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span></span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="154_1_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="154_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:154_1_1_1"/>
( ( <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Maroon" title="c5">X3</font> &amp; not <font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Maroon" title="c5">X3</font> ) or ( not <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Maroon" title="c5">X3</font> &amp; <font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Maroon" title="c5">X3</font> ) or ( <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Maroon" title="c5">X3</font> &amp; <font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Maroon" title="c5">X3</font> ) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:154_1"><span class="lab"><font color="Green" title="E99">A7</font></span></a>, <a class="ref" href="tmap_1.html#T39" target="_self" title="TMAP_1:th.39">Th39</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="154_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:154_1_1_1_1"/><span class="lab"><font color="Green" title="E100">A8</font></span>: 
( <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Maroon" title="c5">X3</font> &amp; not <font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Maroon" title="c5">X3</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c8">f3</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span></span><br/><div class="add"><a NAME="E2:154_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E101">A9</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tmap_1.html#T31" target="_self" title="TMAP_1:th.31">Th31</a></span>;<br/><a NAME="E3:154_1_1_1_1"/><span class="lab"><font color="Green" title="E102">A10</font></span>: 
<font color="Maroon" title="c3">X1</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tsep_1.html#T22" title="TSEP_1:th.22">TSEP_1:22</a></span>;<br/><a NAME="E4:154_1_1_1_1"/>
<font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c3">X1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:154_1_1_1_1"><span class="lab"><font color="Green" title="E100">A8</font></span></a>, <a class="ref" href="tsep_1.html#T30" title="TSEP_1:th.30">TSEP_1:30</a></span>;<br/><span class="kw">then </span><span class="p1">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <font color="Maroon" title="c3">X1</font></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:154_1_1_1_1"><span class="lab"><font color="Green" title="E102">A10</font></span></a>, <a class="ref" href="tmap_1.html#T79" target="_self" title="TMAP_1:th.79">Th79</a></span>
<br/>.= 
<font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:154"><span class="lab"><font color="Green" title="E93">A1</font></span></a>, <a class="ref" href="tmap_1.html#D12" target="_self" title="TMAP_1:def.12">Def12</a></span>
;<br/><span class="kw">hence </span><a NAME="E6:154_1_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c8">f3</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:154"><span class="lab"><font color="Green" title="E94">A2</font></span></a>, <a class="txt" href="#E1:154_1_1_1_1"><span class="lab"><font color="Green" title="E100">A8</font></span></a>, <a class="txt" href="#E2:154_1_1_1_1"><span class="lab"><font color="Green" title="E101">A9</font></span></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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="154_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:154_1_1_1_2"/><span class="lab"><font color="Green" title="E100">A11</font></span>: 
( not <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Maroon" title="c5">X3</font> &amp; <font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Maroon" title="c5">X3</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c8">f3</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span></span><br/><div class="add"><a NAME="E2:154_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E101">A12</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tmap_1.html#T31" target="_self" title="TMAP_1:th.31">Th31</a></span>;<br/><a NAME="E3:154_1_1_1_2"/><span class="lab"><font color="Green" title="E102">A13</font></span>: 
<font color="Maroon" title="c4">X2</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tsep_1.html#T22" title="TSEP_1:th.22">TSEP_1:22</a></span>;<br/><a NAME="E4:154_1_1_1_2"/>
<font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c4">X2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:154_1_1_1_2"><span class="lab"><font color="Green" title="E100">A11</font></span></a>, <a class="ref" href="tsep_1.html#T30" title="TSEP_1:th.30">TSEP_1:30</a></span>;<br/><span class="kw">then </span><span class="p1">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:154_1_1_1_2"><span class="lab"><font color="Green" title="E102">A13</font></span></a>, <a class="ref" href="tmap_1.html#T79" target="_self" title="TMAP_1:th.79">Th79</a></span>
<br/>.= 
<font color="Maroon" title="c7">f2</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:154"><span class="lab"><font color="Green" title="E93">A1</font></span></a>, <a class="ref" href="tmap_1.html#D12" target="_self" title="TMAP_1:def.12">Def12</a></span>
;<br/><span class="kw">hence </span><a NAME="E6:154_1_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c8">f3</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:154"><span class="lab"><font color="Green" title="E95">A3</font></span></a>, <a class="txt" href="#E1:154_1_1_1_2"><span class="lab"><font color="Green" title="E100">A11</font></span></a>, <a class="txt" href="#E2:154_1_1_1_2"><span class="lab"><font color="Green" title="E101">A12</font></span></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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="154_1_1_1_3"><span class="kw">suppose </span></a><a NAME="E1:154_1_1_1_3"/><span class="lab"><font color="Green" title="E100">A14</font></span>: 
( <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Maroon" title="c5">X3</font> &amp; <font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#NR2" title="TSEP_1:NR.2">meets</a> <font color="Maroon" title="c5">X3</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c8">f3</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span></span><br/><div class="add"><a NAME="E2:154_1_1_1_3"/><span class="kw">then </span>
( <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c5">X3</font> &amp; <font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c5">X3</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tsep_1.html#T30" title="TSEP_1:th.30">TSEP_1:30</a></span>;<br/><a NAME="E3:154_1_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E101">A15</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c5">X3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tmap_1.html#T29" target="_self" title="TMAP_1:th.29">Th29</a></span>;<br/><a NAME="E4:154_1_1_1_3"/><span class="lab"><font color="Green" title="E102">A16</font></span>: 
<font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c4">X2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:154_1_1_1_3"><span class="lab"><font color="Green" title="E100">A14</font></span></a>, <a class="ref" href="tsep_1.html#T30" title="TSEP_1:th.30">TSEP_1:30</a></span>;<br/><a NAME="E5:154_1_1_1_3"/><span class="lab"><font color="Green" title="E103">A17</font></span>: 
<font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tsep_1.html#T22" title="TSEP_1:th.22">TSEP_1:22</a></span>;<br/><a NAME="E6:154_1_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E104">A18</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">f3</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span></span>)</span></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c8">f3</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:154_1_1_1_3"><span class="lab"><font color="Green" title="E101">A15</font></span></a>, <a class="ref" href="tmap_1.html#T79" target="_self" title="TMAP_1:th.79">Th79</a></span>;<br/><a NAME="E7:154_1_1_1_3"/><span class="lab"><font color="Green" title="E105">A19</font></span>: 
<font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c3">X1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:154_1_1_1_3"><span class="lab"><font color="Green" title="E100">A14</font></span></a>, <a class="ref" href="tsep_1.html#T30" title="TSEP_1:th.30">TSEP_1:30</a></span>;<br/><a NAME="E8:154_1_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E106">A20</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:154_1_1_1_3"><span class="lab"><font color="Green" title="E102">A16</font></span></a>, <a class="ref" href="tmap_1.html#T27" target="_self" title="TMAP_1:th.27">Th27</a></span>;<br/><a NAME="E9:154_1_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E107">A21</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span></span>)</span></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:154_1_1_1_3"><span class="lab"><font color="Green" title="E103">A17</font></span></a>, <a class="ref" href="tmap_1.html#T79" target="_self" title="TMAP_1:th.79">Th79</a></span>;<br/><a NAME="E10:154_1_1_1_3"/>
<font color="Maroon" title="c4">X2</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tsep_1.html#T22" title="TSEP_1:th.22">TSEP_1:22</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E108">A22</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:154_1_1_1_3"><span class="lab"><font color="Green" title="E102">A16</font></span></a>, <a class="ref" href="tmap_1.html#T79" target="_self" title="TMAP_1:th.79">Th79</a></span>
<br/>.= 
<font color="Maroon" title="c7">f2</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:154"><span class="lab"><font color="Green" title="E93">A1</font></span></a>, <a class="ref" href="tmap_1.html#D12" target="_self" title="TMAP_1:def.12">Def12</a></span>
;<br/><span class="kw">set </span><font color="Maroon" title="c11">v</font> = <font color="Maroon" title="c8">f3</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span></span>)</span>;<br/><a NAME="E12:154_1_1_1_3"/><span class="lab"><font color="Green" title="E109">A23</font></span>: 
<font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tsep_1.html#T22" title="TSEP_1:th.22">TSEP_1:22</a></span>;<br/><a NAME="E13:154_1_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E110">A24</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">f3</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span></span>)</span></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c8">f3</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:154_1_1_1_3"><span class="lab"><font color="Green" title="E101">A15</font></span></a>, <a class="ref" href="tmap_1.html#T79" target="_self" title="TMAP_1:th.79">Th79</a></span>;<br/><a NAME="E14:154_1_1_1_3"/>
<font color="Maroon" title="c3">X1</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tsep_1.html#T22" title="TSEP_1:th.22">TSEP_1:22</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E111">A25</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <font color="Maroon" title="c3">X1</font></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:154_1_1_1_3"><span class="lab"><font color="Green" title="E105">A19</font></span></a>, <a class="ref" href="tmap_1.html#T79" target="_self" title="TMAP_1:th.79">Th79</a></span>
<br/>.= 
<font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:154"><span class="lab"><font color="Green" title="E93">A1</font></span></a>, <a class="ref" href="tmap_1.html#D12" target="_self" title="TMAP_1:def.12">Def12</a></span>
;<br/><a NAME="E16:154_1_1_1_3"/><span class="lab"><font color="Green" title="E112">A26</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span></span>)</span></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:154_1_1_1_3"><span class="lab"><font color="Green" title="E106">A20</font></span></a>, <a class="txt" href="#E12:154_1_1_1_3"><span class="lab"><font color="Green" title="E109">A23</font></span></a>, <a class="ref" href="tmap_1.html#T79" target="_self" title="TMAP_1:th.79">Th79</a></span>;<br/><span class="p1">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:154_1_1_1_3"><span class="lab"><font color="Green" title="E100">A14</font></span></a>, <a class="ref" href="tsep_1.html#T35" title="TSEP_1:th.35">TSEP_1:35</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">f3</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span></span>)</span></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span></span>)</span> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">f3</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span></span>)</span></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:154"><span class="lab"><font color="Green" title="E94">A2</font></span></a>, <a class="txt" href="#E3:154"><span class="lab"><font color="Green" title="E95">A3</font></span></a>, <a class="txt" href="#E1:154_1_1_1_3"><span class="lab"><font color="Green" title="E100">A14</font></span></a>, <a class="txt" href="#E15:154_1_1_1_3"><span class="lab"><font color="Green" title="E111">A25</font></span></a>, <a class="txt" href="#E11:154_1_1_1_3"><span class="lab"><font color="Green" title="E108">A22</font></span></a>, <a class="txt" href="#E9:154_1_1_1_3"><span class="lab"><font color="Green" title="E107">A21</font></span></a>, <a class="txt" href="#E16:154_1_1_1_3"><span class="lab"><font color="Green" title="E112">A26</font></span></a>, <a class="txt" href="#E6:154_1_1_1_3"><span class="lab"><font color="Green" title="E104">A18</font></span></a>, <a class="txt" href="#E13:154_1_1_1_3"><span class="lab"><font color="Green" title="E110">A24</font></span></a>, <a class="ref" href="tmap_1.html#T138" target="_self" title="TMAP_1:th.138">Th138</a></span>
<br/>.= 
<font color="Maroon" title="c8">f3</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="tmap_1.html#T138" target="_self" title="TMAP_1:th.138">Th138</a></span>
;<br/><span class="kw">hence </span><a NAME="E18:154_1_1_1_3"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c8">f3</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:154_1_1_1_3"><span class="lab"><font color="Green" title="E100">A14</font></span></a>, <a class="ref" href="tsep_1.html#T35" title="TSEP_1:th.35">TSEP_1:35</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/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E3:154_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c8">f3</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="tsep_1.html#K2" title="TSEP_1:func.2">meet</a> <font color="Maroon" title="c5">X3</font></span>)</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/></div><span class="kw">end;</span></div>
<a NAME="E8:154"/><span class="kw">then </span>
( <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c5">X3</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c8">f3</font></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tmap_1.html#D12" target="_self" title="TMAP_1:def.12">Def12</a>, <a class="ref" href="tsep_1.html#T22" title="TSEP_1:th.22">TSEP_1:22</a></span>;<br/>
<a NAME="E9:154"/><span class="kw">then </span><span class="lab"><font color="Green" title="E99">A27</font></span>: 
<font color="Maroon" title="c10">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tmap_1.html#D4" target="_self" title="TMAP_1:def.4">Def4</a></span>;<br/>
<a NAME="E10:154"/><span class="lab"><font color="Green" title="E100">A28</font></span>: 
<font color="Maroon" title="c5">X3</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c5">X3</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:154"><span class="lab"><font color="Green" title="E96">A4</font></span></a>, <a class="ref" href="tsep_1.html#T22" title="TSEP_1:th.22">TSEP_1:22</a></span>;<br/>
<a NAME="E11:154"/><span class="lab"><font color="Green" title="E101">A29</font></span>: 
<font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c5">X3</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c5">X3</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tsep_1.html#T22" title="TSEP_1:th.22">TSEP_1:22</a></span>;<br/>
<a NAME="E12:154"/>
( <font color="Maroon" title="c5">X3</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font></span>)</span> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c5">X3</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c8">f3</font></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <font color="Maroon" title="c5">X3</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c8">f3</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:154"><span class="lab"><font color="Green" title="E98">A6</font></span></a>, <a class="ref" href="tmap_1.html#D12" target="_self" title="TMAP_1:def.12">Def12</a>, <a class="ref" href="tsep_1.html#T22" title="TSEP_1:th.22">TSEP_1:22</a></span>;<br/>
<a NAME="E13:154"/><span class="kw">then </span><span class="lab"><font color="Green" title="E102">A30</font></span>: 
<font color="Maroon" title="c10">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">X3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">f3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tmap_1.html#D4" target="_self" title="TMAP_1:def.4">Def4</a></span>;<br/>
<a NAME="E14:154"/><span class="lab"><font color="Green" title="E103">A31</font></span>: 
<font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c5">X3</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:154"><span class="lab"><font color="Green" title="E96">A4</font></span></a>, <a class="ref" href="tsep_1.html#T22" title="TSEP_1:th.22">TSEP_1:22</a></span>;<br/>
<a NAME="E15:154"/>
<font color="Maroon" title="c5">X3</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c5">X3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tsep_1.html#T22" title="TSEP_1:th.22">TSEP_1:22</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E104">A32</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c10">f</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c5">X3</font></span>)</span></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <font color="Maroon" title="c5">X3</font> = 
<font color="Maroon" title="c10">f</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <font color="Maroon" title="c5">X3</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:154"><span class="lab"><font color="Green" title="E101">A29</font></span></a>, <a class="ref" href="tmap_1.html#T79" target="_self" title="TMAP_1:th.79">Th79</a></span>
<br/>.= 
<font color="Maroon" title="c8">f3</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:154"><span class="lab"><font color="Green" title="E100">A28</font></span></a>, <a class="txt" href="#E13:154"><span class="lab"><font color="Green" title="E102">A30</font></span></a>, <a class="ref" href="tmap_1.html#D4" target="_self" title="TMAP_1:def.4">Def4</a></span>
;<br/>
<a NAME="E17:154"/>
<font color="Maroon" title="c4">X2</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tsep_1.html#T22" title="TSEP_1:th.22">TSEP_1:22</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E105">A33</font></span>: <font color="Maroon" title="c10">f</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <font color="Maroon" title="c4">X2</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">f</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font></span>)</span></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <font color="Maroon" title="c4">X2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:154"><span class="lab"><font color="Green" title="E103">A31</font></span></a>, <a class="ref" href="tmap_1.html#T79" target="_self" title="TMAP_1:th.79">Th79</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <font color="Maroon" title="c4">X2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:154"><span class="lab"><font color="Green" title="E97">A5</font></span></a>, <a class="txt" href="#E9:154"><span class="lab"><font color="Green" title="E99">A27</font></span></a>, <a class="ref" href="tmap_1.html#D4" target="_self" title="TMAP_1:def.4">Def4</a></span>
;<br/>
<a NAME="E19:154"/>
<font color="Maroon" title="c4">X2</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c5">X3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tsep_1.html#T22" title="TSEP_1:th.22">TSEP_1:22</a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><font color="Maroon" title="c10">f</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c5">X3</font></span>)</span></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <font color="Maroon" title="c4">X2</font> = 
<font color="Maroon" title="c10">f</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <font color="Maroon" title="c4">X2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:154"><span class="lab"><font color="Green" title="E101">A29</font></span></a>, <a class="ref" href="tmap_1.html#T79" target="_self" title="TMAP_1:th.79">Th79</a></span>
<br/>.= 
<font color="Maroon" title="c7">f2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:154"><span class="lab"><font color="Green" title="E93">A1</font></span></a>, <a class="txt" href="#E18:154"><span class="lab"><font color="Green" title="E105">A33</font></span></a>, <a class="ref" href="tmap_1.html#D12" target="_self" title="TMAP_1:def.12">Def12</a></span>
;<br/>
<a NAME="E21:154"/><span class="kw">then </span><span class="lab"><font color="Green" title="E106">A34</font></span>: 
<font color="Maroon" title="c10">f</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X2</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c5">X3</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c7">f2</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c8">f3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:154"><span class="lab"><font color="Green" title="E104">A32</font></span></a>, <a class="ref" href="tmap_1.html#T138" target="_self" title="TMAP_1:th.138">Th138</a></span>;<br/>
<a NAME="E22:154"/>
<font color="Maroon" title="c3">X1</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tsep_1.html#T22" title="TSEP_1:th.22">TSEP_1:22</a></span>;<br/>
<span class="kw">then </span><font color="Maroon" title="c10">f</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <font color="Maroon" title="c3">X1</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">f</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">X1</font> <a href="tsep_1.html#K1" title="TSEP_1:func.1">union</a> <font color="Maroon" title="c4">X2</font></span>)</span></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <font color="Maroon" title="c3">X1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:154"><span class="lab"><font color="Green" title="E103">A31</font></span></a>, <a class="ref" href="tmap_1.html#T79" target="_self" title="TMAP_1:th.79">Th79</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <font color="Maroon" title="c3">X1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:154"><span class="lab"><font color="Green" title="E97">A5</font></span></a>, <a class="txt" href="#E9:154"><span class="lab"><font color="Green" title="E99">A27</font></span></a>, <a class="ref" href="tmap_1.html#D4" target="_self" title="TMAP_1:def.4">Def4</a></span>
;<br/>
<a NAME="E24:154"/><span class="kw">then </span>
<font color="Maroon" title="c10">f</font> <a href="tmap_1.html#K3" title="TMAP_1:func.3">|</a> <font color="Maroon" title="c3">X1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c6">f1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:154"><span class="lab"><font color="Green" title="E93">A1</font></span></a>, <a class="ref" href="tmap_1.html#D12" target="_self" title="TMAP_1:def.12">Def12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E25:154"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c7">f2</font></span>)</span> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c8">f3</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c6">f1</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="tmap_1.html#K10" title="TMAP_1:func.10">union</a> <font color="Maroon" title="c8">f3</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:154"><span class="lab"><font color="Green" title="E106">A34</font></span></a>, <a class="ref" href="tmap_1.html#T138" target="_self" title="TMAP_1:th.138">Th138</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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