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<span class="kw">let </span><font color="Maroon" title="c1">k</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">V</font> being   <a href="rltopsp1.html#NM1" title="RLTOPSP1:NM.1">LinearTopSpace</a><br/>  for <font color="Olive" title="b2">A</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   <a href="rlaffin1.html#V1" title="RLAFFIN1:attr.1">affinely-independent</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">V</font><br/>  for <font color="Olive" title="b3">E</font> being    <a href="rlaffin3.html#M2" title="RLAFFIN3:mode.2">Enumeration</a> of <font color="Olive" title="b2">A</font><br/>  for <font color="Olive" title="b4">v</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">V</font><br/>  for <font color="Olive" title="b5">Ev</font> being    <a href="rlaffin3.html#M2" title="RLAFFIN3:mode.2">Enumeration</a> of <font color="Olive" title="b4">v</font> <a href="rusub_4.html#K5" title="RUSUB_4:func.5">+</a> <font color="Olive" title="b2">A</font>  st <font color="Olive" title="b5">Ev</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">E</font> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b2">A</font></span>)</span> <a href="finseq_2.html#K5" title="FINSEQ_2:func.5">|-&gt;</a> <font color="Olive" title="b4">v</font></span>)</span> holds <br/> for <font color="Olive" title="b6">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds  <span class="p1">(<span class="default"><a href="rltopsp1.html#K3" title="RLTOPSP1:func.3">transl</a> (<font color="Olive" title="b4">v</font>,<font color="Olive" title="b1">V</font>)</span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b7">u</font> where <font color="Olive" title="b7">u</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">V</font> : ( <font color="Olive" title="b7">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <font color="Olive" title="b2">A</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b7">u</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Olive" title="b3">E</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b6">X</font> ) </span> } </span>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b7">w</font> where <font color="Olive" title="b7">w</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">V</font> : ( <font color="Olive" title="b7">w</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">v</font> <a href="rusub_4.html#K5" title="RUSUB_4:func.5">+</a> <font color="Olive" title="b2">A</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b7">w</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Olive" title="b5">Ev</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b6">X</font> ) </span> } </span> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">V</font> be   <a href="rltopsp1.html#NM1" title="RLTOPSP1:NM.1">LinearTopSpace</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">A</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   <a href="rlaffin1.html#V1" title="RLAFFIN1:attr.1">affinely-independent</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">V</font><br/>  for <font color="Olive" title="b2">E</font> being    <a href="rlaffin3.html#M2" title="RLAFFIN3:mode.2">Enumeration</a> of <font color="Olive" title="b1">A</font><br/>  for <font color="Olive" title="b3">v</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font><br/>  for <font color="Olive" title="b4">Ev</font> being    <a href="rlaffin3.html#M2" title="RLAFFIN3:mode.2">Enumeration</a> of <font color="Olive" title="b3">v</font> <a href="rusub_4.html#K5" title="RUSUB_4:func.5">+</a> <font color="Olive" title="b1">A</font>  st <font color="Olive" title="b4">Ev</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">E</font> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="finseq_2.html#K5" title="FINSEQ_2:func.5">|-&gt;</a> <font color="Olive" title="b3">v</font></span>)</span> holds <br/> for <font color="Olive" title="b5">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds  <span class="p1">(<span class="default"><a href="rltopsp1.html#K3" title="RLTOPSP1:func.3">transl</a> (<font color="Olive" title="b3">v</font>,<font color="Maroon" title="c2">V</font>)</span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b6">u</font> where <font color="Olive" title="b6">u</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : ( <font color="Olive" title="b6">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <font color="Olive" title="b1">A</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b6">u</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Olive" title="b2">E</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b5">X</font> ) </span> } </span>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b6">w</font> where <font color="Olive" title="b6">w</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : ( <font color="Olive" title="b6">w</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">v</font> <a href="rusub_4.html#K5" title="RUSUB_4:func.5">+</a> <font color="Olive" title="b1">A</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b6">w</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Olive" title="b4">Ev</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b5">X</font> ) </span> } </span> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">A</font> be   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   <a href="rlaffin1.html#V1" title="RLAFFIN1:attr.1">affinely-independent</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">V</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">E</font> being    <a href="rlaffin3.html#M2" title="RLAFFIN3:mode.2">Enumeration</a> of <font color="Maroon" title="c3">A</font><br/>  for <font color="Olive" title="b2">v</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font><br/>  for <font color="Olive" title="b3">Ev</font> being    <a href="rlaffin3.html#M2" title="RLAFFIN3:mode.2">Enumeration</a> of <font color="Olive" title="b2">v</font> <a href="rusub_4.html#K5" title="RUSUB_4:func.5">+</a> <font color="Maroon" title="c3">A</font>  st <font color="Olive" title="b3">Ev</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">E</font> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="finseq_2.html#K5" title="FINSEQ_2:func.5">|-&gt;</a> <font color="Olive" title="b2">v</font></span>)</span> holds <br/> for <font color="Olive" title="b4">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds  <span class="p1">(<span class="default"><a href="rltopsp1.html#K3" title="RLTOPSP1:func.3">transl</a> (<font color="Olive" title="b2">v</font>,<font color="Maroon" title="c2">V</font>)</span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b5">u</font> where <font color="Olive" title="b5">u</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : ( <font color="Olive" title="b5">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <font color="Maroon" title="c3">A</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b5">u</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Olive" title="b1">E</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">X</font> ) </span> } </span>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b5">w</font> where <font color="Olive" title="b5">w</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : ( <font color="Olive" title="b5">w</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">v</font> <a href="rusub_4.html#K5" title="RUSUB_4:func.5">+</a> <font color="Maroon" title="c3">A</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b5">w</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Olive" title="b3">Ev</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">X</font> ) </span> } </span> </span><br/><span class="kw">let </span><font color="Maroon" title="c4">E</font> be    <a href="rlaffin3.html#M2" title="RLAFFIN3:mode.2">Enumeration</a> of <font color="Maroon" title="c3">A</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">v</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font><br/>  for <font color="Olive" title="b2">Ev</font> being    <a href="rlaffin3.html#M2" title="RLAFFIN3:mode.2">Enumeration</a> of <font color="Olive" title="b1">v</font> <a href="rusub_4.html#K5" title="RUSUB_4:func.5">+</a> <font color="Maroon" title="c3">A</font>  st <font color="Olive" title="b2">Ev</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">E</font> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="finseq_2.html#K5" title="FINSEQ_2:func.5">|-&gt;</a> <font color="Olive" title="b1">v</font></span>)</span> holds <br/> for <font color="Olive" title="b3">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds  <span class="p1">(<span class="default"><a href="rltopsp1.html#K3" title="RLTOPSP1:func.3">transl</a> (<font color="Olive" title="b1">v</font>,<font color="Maroon" title="c2">V</font>)</span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b4">u</font> where <font color="Olive" title="b4">u</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : ( <font color="Olive" title="b4">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <font color="Maroon" title="c3">A</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b4">u</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">X</font> ) </span> } </span>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b4">w</font> where <font color="Olive" title="b4">w</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : ( <font color="Olive" title="b4">w</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">v</font> <a href="rusub_4.html#K5" title="RUSUB_4:func.5">+</a> <font color="Maroon" title="c3">A</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b4">w</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Olive" title="b2">Ev</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">X</font> ) </span> } </span> </span><br/><span class="kw">let </span><font color="Maroon" title="c5">v</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">Ev</font> being    <a href="rlaffin3.html#M2" title="RLAFFIN3:mode.2">Enumeration</a> of <font color="Maroon" title="c5">v</font> <a href="rusub_4.html#K5" title="RUSUB_4:func.5">+</a> <font color="Maroon" title="c3">A</font>  st <font color="Olive" title="b1">Ev</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">E</font> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="finseq_2.html#K5" title="FINSEQ_2:func.5">|-&gt;</a> <font color="Maroon" title="c5">v</font></span>)</span> holds <br/> for <font color="Olive" title="b2">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds  <span class="p1">(<span class="default"><a href="rltopsp1.html#K3" title="RLTOPSP1:func.3">transl</a> (<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c2">V</font>)</span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b3">u</font> where <font color="Olive" title="b3">u</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : ( <font color="Olive" title="b3">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <font color="Maroon" title="c3">A</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b3">u</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">X</font> ) </span> } </span>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b3">w</font> where <font color="Olive" title="b3">w</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : ( <font color="Olive" title="b3">w</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="rusub_4.html#K5" title="RUSUB_4:func.5">+</a> <font color="Maroon" title="c3">A</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b3">w</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Olive" title="b1">Ev</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">X</font> ) </span> } </span> </span><br/><span class="kw">let </span><font color="Maroon" title="c6">Ev</font> be    <a href="rlaffin3.html#M2" title="RLAFFIN3:mode.2">Enumeration</a> of <font color="Maroon" title="c5">v</font> <a href="rusub_4.html#K5" title="RUSUB_4:func.5">+</a> <font color="Maroon" title="c3">A</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c6">Ev</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">E</font> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="finseq_2.html#K5" title="FINSEQ_2:func.5">|-&gt;</a> <font color="Maroon" title="c5">v</font></span>)</span> implies  for <font color="Olive" title="b1">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds  <span class="p1">(<span class="default"><a href="rltopsp1.html#K3" title="RLTOPSP1:func.3">transl</a> (<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c2">V</font>)</span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b2">u</font> where <font color="Olive" title="b2">u</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : ( <font color="Olive" title="b2">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <font color="Maroon" title="c3">A</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b2">u</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">X</font> ) </span> } </span>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b2">w</font> where <font color="Olive" title="b2">w</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : ( <font color="Olive" title="b2">w</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="rusub_4.html#K5" title="RUSUB_4:func.5">+</a> <font color="Maroon" title="c3">A</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b2">w</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Maroon" title="c6">Ev</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">X</font> ) </span> } </span>  )</span><br/>











<span class="kw">assume </span><a NAME="E1:37"/><span class="lab"><font color="Green" title="E29">A1</font></span>: 
<font color="Maroon" title="c6">Ev</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">E</font> <a href="fvsum_1.html#K3" title="FVSUM_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="finseq_2.html#K5" title="FINSEQ_2:func.5">|-&gt;</a> <font color="Maroon" title="c5">v</font></span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds  <span class="p1">(<span class="default"><a href="rltopsp1.html#K3" title="RLTOPSP1:func.3">transl</a> (<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c2">V</font>)</span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b2">u</font> where <font color="Olive" title="b2">u</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : ( <font color="Olive" title="b2">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <font color="Maroon" title="c3">A</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b2">u</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">X</font> ) </span> } </span>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b2">w</font> where <font color="Olive" title="b2">w</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : ( <font color="Olive" title="b2">w</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="rusub_4.html#K5" title="RUSUB_4:func.5">+</a> <font color="Maroon" title="c3">A</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b2">w</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Maroon" title="c6">Ev</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">X</font> ) </span> } </span> </span><br/>

<span class="kw">set </span><font color="Maroon" title="c7">T</font> =  <a href="rltopsp1.html#K3" title="RLTOPSP1:func.3">transl</a> (<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c2">V</font>);<br/>
<span class="kw">let </span><font color="Maroon" title="c8">X</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="rltopsp1.html#K3" title="RLTOPSP1:func.3">transl</a> (<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c2">V</font>)</span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">u</font> where <font color="Olive" title="b1">u</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : ( <font color="Olive" title="b1">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <font color="Maroon" title="c3">A</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">X</font> ) </span> } </span>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">w</font> where <font color="Olive" title="b1">w</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : ( <font color="Olive" title="b1">w</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="rusub_4.html#K5" title="RUSUB_4:func.5">+</a> <font color="Maroon" title="c3">A</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">w</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Maroon" title="c6">Ev</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">X</font> ) </span> } </span> </span><br/>

<span class="kw">set </span><font color="Maroon" title="c9">U</font> = <span class="p1"> { <span class="default"> <font color="Olive" title="b1">u</font> where <font color="Olive" title="b1">u</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : ( <font color="Olive" title="b1">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <font color="Maroon" title="c3">A</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">X</font> ) </span> } </span> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">W</font> = <span class="p1"> { <span class="default"> <font color="Olive" title="b1">w</font> where <font color="Olive" title="b1">w</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : ( <font color="Olive" title="b1">w</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="rusub_4.html#K5" title="RUSUB_4:func.5">+</a> <font color="Maroon" title="c3">A</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">w</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Maroon" title="c6">Ev</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">X</font> ) </span> } </span> ;<br/>
<a NAME="E2:37"/><span class="lab"><font color="Green" title="E30">A2</font></span>: 
 <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="rusub_4.html#K5" title="RUSUB_4:func.5">+</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font> <a href="rusub_4.html#K5" title="RUSUB_4:func.5">+</a> <span class="p1">(<span class="default"><a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <font color="Maroon" title="c3">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlaffin1.html#T53" onmouseover="rs('rlaffin1/T53')" onmouseout="rh()">RLAFFIN1:53</a></span>;<br/>
<div><span class="kw">hereby </span> <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</a>,<a class="ref" href="xboole_0.html#D10" onmouseover="rs('xboole_0/D10')" onmouseout="rh()">XBOOLE_0:def 10</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">w</font> where <font color="Olive" title="b1">w</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : ( <font color="Olive" title="b1">w</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="rusub_4.html#K5" title="RUSUB_4:func.5">+</a> <font color="Maroon" title="c3">A</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">w</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Maroon" title="c6">Ev</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">X</font> ) </span> } </span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="rltopsp1.html#K3" title="RLTOPSP1:func.3">transl</a> (<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c2">V</font>)</span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">u</font> where <font color="Olive" title="b1">u</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : ( <font color="Olive" title="b1">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <font color="Maroon" title="c3">A</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">X</font> ) </span> } </span> </span>
<div class="add"><span class="kw">let </span><font color="Maroon" title="c11">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c11">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="rltopsp1.html#K3" title="RLTOPSP1:func.3">transl</a> (<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c2">V</font>)</span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">u</font> where <font color="Olive" title="b1">u</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : ( <font color="Olive" title="b1">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <font color="Maroon" title="c3">A</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">X</font> ) </span> } </span>  implies <font color="Maroon" title="c11">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">w</font> where <font color="Olive" title="b1">w</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : ( <font color="Olive" title="b1">w</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="rusub_4.html#K5" title="RUSUB_4:func.5">+</a> <font color="Maroon" title="c3">A</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">w</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Maroon" title="c6">Ev</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">X</font> ) </span> } </span>  )</span><br/><span class="kw">assume </span><a NAME="E1:37_1"/>
<font color="Maroon" title="c11">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="rltopsp1.html#K3" title="RLTOPSP1:func.3">transl</a> (<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c2">V</font>)</span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">u</font> where <font color="Olive" title="b1">u</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : ( <font color="Olive" title="b1">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <font color="Maroon" title="c3">A</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">X</font> ) </span> } </span> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c11">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">w</font> where <font color="Olive" title="b1">w</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : ( <font color="Olive" title="b1">w</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="rusub_4.html#K5" title="RUSUB_4:func.5">+</a> <font color="Maroon" title="c3">A</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">w</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Maroon" title="c6">Ev</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">X</font> ) </span> } </span> </span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c12">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E3:37_1"/>
<font color="Maroon" title="c12">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="rltopsp1.html#K3" title="RLTOPSP1:func.3">transl</a> (<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c2">V</font>)</span>)</span>
 <span class="kw">and </span><br/><a NAME="E4:37_1"/><span class="lab"><font color="Green" title="E31">A3</font></span>: 
<font color="Maroon" title="c12">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">u</font> where <font color="Olive" title="b1">u</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : ( <font color="Olive" title="b1">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <font color="Maroon" title="c3">A</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">X</font> ) </span> } </span> 
 <span class="kw">and </span><br/><a NAME="E5:37_1"/><span class="lab"><font color="Green" title="E32">A4</font></span>: 
<span class="p1">(<span class="default"><a href="rltopsp1.html#K3" title="RLTOPSP1:func.3">transl</a> (<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c2">V</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">y</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D6" onmouseover="rs('funct_1/D6')" onmouseout="rh()">FUNCT_1:def 6</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c13">u</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font><span class="kw"> such that </span><br/><a NAME="E7:37_1"/><span class="lab"><font color="Green" title="E33">A5</font></span>: 
<font color="Maroon" title="c12">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">u</font>
 <span class="kw">and </span><br/><a NAME="E8:37_1"/><span class="lab"><font color="Green" title="E34">A6</font></span>: 
<font color="Maroon" title="c13">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <font color="Maroon" title="c3">A</font>
 <span class="kw">and </span><br/><a NAME="E9:37_1"/><span class="lab"><font color="Green" title="E35">A7</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c13">u</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">X</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:37_1"><span class="lab"><font color="Green" title="E31">A3</font></span></a></span>;<br/><a NAME="E10:37_1"/>
<font color="Maroon" title="c5">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c13">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b1">t</font></span>)</span> where <font color="Olive" title="b1">t</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : <font color="Olive" title="b1">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <font color="Maroon" title="c3">A</font> </span> } </span> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:37_1"><span class="lab"><font color="Green" title="E34">A6</font></span></a></span>;<br/><a NAME="E11:37_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A8</font></span>: 
<font color="Maroon" title="c5">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c13">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="rusub_4.html#K5" title="RUSUB_4:func.5">+</a> <font color="Maroon" title="c3">A</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:37"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="ref" href="rusub_4.html#D8" onmouseover="rs('rusub_4/D8')" onmouseout="rh()">RUSUB_4:def 8</a></span>;<br/><a NAME="E12:37_1"/>
<font color="Maroon" title="c13">u</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Maroon" title="c4">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c13">u</font></span>)</span> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Maroon" title="c6">Ev</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="txt" href="#E8:37_1"><span class="lab"><font color="Green" title="E34">A6</font></span></a>, <a class="ref" href="rlaffin3.html#T17" target="_self" onmouseover="rs('rlaffin3/T17')" onmouseout="rh()">Th17</a></span>;<br/><a NAME="E13:37_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c13">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">w</font> where <font color="Olive" title="b1">w</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : ( <font color="Olive" title="b1">w</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="rusub_4.html#K5" title="RUSUB_4:func.5">+</a> <font color="Maroon" title="c3">A</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">w</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Maroon" title="c6">Ev</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">X</font> ) </span> } </span> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:37_1"><span class="lab"><font color="Green" title="E35">A7</font></span></a>, <a class="txt" href="#E11:37_1"><span class="lab"><font color="Green" title="E36">A8</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E14:37_1"/>
<font color="Maroon" title="c11">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">w</font> where <font color="Olive" title="b1">w</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : ( <font color="Olive" title="b1">w</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="rusub_4.html#K5" title="RUSUB_4:func.5">+</a> <font color="Maroon" title="c3">A</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">w</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Maroon" title="c6">Ev</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">X</font> ) </span> } </span> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:37_1"><span class="lab"><font color="Green" title="E32">A4</font></span></a>, <a class="txt" href="#E7:37_1"><span class="lab"><font color="Green" title="E33">A5</font></span></a>, <a class="ref" href="rltopsp1.html#D10" onmouseover="rs('rltopsp1/D10')" onmouseout="rh()">RLTOPSP1:def 10</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>

<span class="kw">let </span><font color="Maroon" title="c11">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c11">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">w</font> where <font color="Olive" title="b1">w</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : ( <font color="Olive" title="b1">w</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="rusub_4.html#K5" title="RUSUB_4:func.5">+</a> <font color="Maroon" title="c3">A</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">w</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Maroon" title="c6">Ev</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">X</font> ) </span> } </span>  or <font color="Maroon" title="c11">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="rltopsp1.html#K3" title="RLTOPSP1:func.3">transl</a> (<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c2">V</font>)</span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">u</font> where <font color="Olive" title="b1">u</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : ( <font color="Olive" title="b1">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <font color="Maroon" title="c3">A</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">X</font> ) </span> } </span>  )</span><br/>

<span class="kw">assume </span><a NAME="E4:37"/>
<font color="Maroon" title="c11">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">w</font> where <font color="Olive" title="b1">w</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : ( <font color="Olive" title="b1">w</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="rusub_4.html#K5" title="RUSUB_4:func.5">+</a> <font color="Maroon" title="c3">A</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">w</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Maroon" title="c6">Ev</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">X</font> ) </span> } </span> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c11">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="rltopsp1.html#K3" title="RLTOPSP1:func.3">transl</a> (<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c2">V</font>)</span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">u</font> where <font color="Olive" title="b1">u</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : ( <font color="Olive" title="b1">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <font color="Maroon" title="c3">A</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">X</font> ) </span> } </span> </span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c12">w</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font><span class="kw"> such that </span><br/><a NAME="E6:37"/><span class="lab"><font color="Green" title="E31">A9</font></span>: 
<font color="Maroon" title="c11">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">w</font>
 <span class="kw">and </span><br/><a NAME="E7:37"/><span class="lab"><font color="Green" title="E32">A10</font></span>: 
<font color="Maroon" title="c12">w</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="rusub_4.html#K5" title="RUSUB_4:func.5">+</a> <font color="Maroon" title="c3">A</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E8:37"/><span class="lab"><font color="Green" title="E33">A11</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c12">w</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Maroon" title="c6">Ev</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">X</font>
 ;<br/>
<a NAME="E9:37"/>
<font color="Maroon" title="c12">w</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b1">t</font></span>)</span> where <font color="Olive" title="b1">t</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : <font color="Olive" title="b1">t</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <font color="Maroon" title="c3">A</font> </span> } </span> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:37"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="txt" href="#E7:37"><span class="lab"><font color="Green" title="E32">A10</font></span></a>, <a class="ref" href="rusub_4.html#D8" onmouseover="rs('rusub_4/D8')" onmouseout="rh()">RUSUB_4:def 8</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c13">u</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font><span class="kw"> such that </span><br/><a NAME="E11:37"/><span class="lab"><font color="Green" title="E34">A12</font></span>: 
<font color="Maroon" title="c12">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c13">u</font>
 <span class="kw">and </span><br/><a NAME="E12:37"/><span class="lab"><font color="Green" title="E35">A13</font></span>: 
<font color="Maroon" title="c13">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <font color="Maroon" title="c3">A</font>
 ;<br/>
<a NAME="E13:37"/>
<font color="Maroon" title="c12">w</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Maroon" title="c6">Ev</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">u</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Maroon" title="c4">E</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="txt" href="#E11:37"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="txt" href="#E12:37"><span class="lab"><font color="Green" title="E35">A13</font></span></a>, <a class="ref" href="rlaffin3.html#T17" target="_self" onmouseover="rs('rlaffin3/T17')" onmouseout="rh()">Th17</a></span>;<br/>
<a NAME="E14:37"/><span class="kw">then </span>
(  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="rltopsp1.html#K3" title="RLTOPSP1:func.3">transl</a> (<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c2">V</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">V</font> &amp; <font color="Maroon" title="c13">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">u</font> where <font color="Olive" title="b1">u</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : ( <font color="Olive" title="b1">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <font color="Maroon" title="c3">A</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">X</font> ) </span> } </span>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:37"><span class="lab"><font color="Green" title="E33">A11</font></span></a>, <a class="txt" href="#E12:37"><span class="lab"><font color="Green" title="E35">A13</font></span></a>, <a class="ref" href="funct_2.html#T52" onmouseover="rs('funct_2/T52')" onmouseout="rh()">FUNCT_2:52</a></span>;<br/>
<a NAME="E15:37"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="rltopsp1.html#K3" title="RLTOPSP1:func.3">transl</a> (<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c2">V</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c13">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="rltopsp1.html#K3" title="RLTOPSP1:func.3">transl</a> (<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c2">V</font>)</span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">u</font> where <font color="Olive" title="b1">u</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : ( <font color="Olive" title="b1">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <font color="Maroon" title="c3">A</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">X</font> ) </span> } </span> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D6" onmouseover="rs('funct_1/D6')" onmouseout="rh()">FUNCT_1:def 6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E16:37"/>
<font color="Maroon" title="c11">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="rltopsp1.html#K3" title="RLTOPSP1:func.3">transl</a> (<font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c2">V</font>)</span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">u</font> where <font color="Olive" title="b1">u</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">V</font> : ( <font color="Olive" title="b1">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rlaffin1.html#K4" title="RLAFFIN1:func.4">Affin</a> <font color="Maroon" title="c3">A</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">u</font> <a href="rlaffin3.html#K1" title="RLAFFIN3:func.1">|--</a> <font color="Maroon" title="c4">E</font></span>)</span> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c8">X</font> ) </span> } </span> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:37"><span class="lab"><font color="Green" title="E31">A9</font></span></a>, <a class="txt" href="#E11:37"><span class="lab"><font color="Green" title="E34">A12</font></span></a>, <a class="ref" href="rltopsp1.html#D10" onmouseover="rs('rltopsp1/D10')" onmouseout="rh()">RLTOPSP1:def 10</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
