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<span class="kw">let </span><font color="Maroon" title="c1">F</font> be   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</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">E</font> being  <font color="Maroon" title="c1">F</font> <a href="field_4.html#V2" title="FIELD_4:attr.2">-finite</a>  <a href="field_4.html#NM4" title="FIELD_4:NM.4">FieldExtension</a> of <font color="Maroon" title="c1">F</font><br/>  for <font color="Olive" title="b2">K</font> being  <font color="Maroon" title="c1">F</font> <a href="field_4.html#V1" title="FIELD_4:attr.1">-extending</a>  <font color="Olive">b<sub>1</sub></font> <a href="field_4.html#V2" title="FIELD_4:attr.2">-finite</a>  <a href="field_4.html#NM4" title="FIELD_4:NM.4">FieldExtension</a> of <font color="Maroon" title="c1">F</font><br/>  for <font color="Olive" title="b3">BE</font> being   <a href="vectsp_7.html#NM1" title="VECTSP_7:NM.1">Basis</a> of <span class="p1">(<span class="default"><a href="field_4.html#K2" title="FIELD_4:func.2">VecSp</a> (<font color="Olive" title="b1">E</font>,<font color="Maroon" title="c1">F</font>)</span>)</span><br/>  for <font color="Olive" title="b4">BK</font> being   <a href="vectsp_7.html#NM1" title="VECTSP_7:NM.1">Basis</a> of <span class="p1">(<span class="default"><a href="field_4.html#K2" title="FIELD_4:func.2">VecSp</a> (<font color="Olive" title="b2">K</font>,<font color="Olive" title="b1">E</font>)</span>)</span><br/>  for <font color="Olive" title="b5">l</font> being    <a href="vectsp_6.html#M2" title="VECTSP_6:mode.2">Linear_Combination</a> of  <a href="field_7.html#K7" title="FIELD_7:func.7">Base</a> (<font color="Olive" title="b3">BE</font>,<font color="Olive" title="b4">BK</font>) holds   <a href="field_7.html#K10" title="FIELD_7:func.10">lift</a> (<span class="p1">(<span class="default"><a href="field_7.html#K9" title="FIELD_7:func.9">down</a> <font color="Olive" title="b5">l</font></span>)</span>,<font color="Olive" title="b3">BE</font>) <a href="vectsp_6.html#R1" title="VECTSP_6:pred.1">=</a> <font color="Olive" title="b5">l</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">E</font> be  <font color="Maroon" title="c1">F</font> <a href="field_4.html#V2" title="FIELD_4:attr.2">-finite</a>  <a href="field_4.html#NM4" title="FIELD_4:NM.4">FieldExtension</a> of <font color="Maroon" title="c1">F</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">K</font> being  <font color="Maroon" title="c1">F</font> <a href="field_4.html#V1" title="FIELD_4:attr.1">-extending</a>  <font color="Maroon" title="c2">E</font> <a href="field_4.html#V2" title="FIELD_4:attr.2">-finite</a>  <a href="field_4.html#NM4" title="FIELD_4:NM.4">FieldExtension</a> of <font color="Maroon" title="c1">F</font><br/>  for <font color="Olive" title="b2">BE</font> being   <a href="vectsp_7.html#NM1" title="VECTSP_7:NM.1">Basis</a> of <span class="p1">(<span class="default"><a href="field_4.html#K2" title="FIELD_4:func.2">VecSp</a> (<font color="Maroon" title="c2">E</font>,<font color="Maroon" title="c1">F</font>)</span>)</span><br/>  for <font color="Olive" title="b3">BK</font> being   <a href="vectsp_7.html#NM1" title="VECTSP_7:NM.1">Basis</a> of <span class="p1">(<span class="default"><a href="field_4.html#K2" title="FIELD_4:func.2">VecSp</a> (<font color="Olive" title="b1">K</font>,<font color="Maroon" title="c2">E</font>)</span>)</span><br/>  for <font color="Olive" title="b4">l</font> being    <a href="vectsp_6.html#M2" title="VECTSP_6:mode.2">Linear_Combination</a> of  <a href="field_7.html#K7" title="FIELD_7:func.7">Base</a> (<font color="Olive" title="b2">BE</font>,<font color="Olive" title="b3">BK</font>) holds   <a href="field_7.html#K10" title="FIELD_7:func.10">lift</a> (<span class="p1">(<span class="default"><a href="field_7.html#K9" title="FIELD_7:func.9">down</a> <font color="Olive" title="b4">l</font></span>)</span>,<font color="Olive" title="b2">BE</font>) <a href="vectsp_6.html#R1" title="VECTSP_6:pred.1">=</a> <font color="Olive" title="b4">l</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">K</font> be  <font color="Maroon" title="c1">F</font> <a href="field_4.html#V1" title="FIELD_4:attr.1">-extending</a>  <font color="Maroon" title="c2">E</font> <a href="field_4.html#V2" title="FIELD_4:attr.2">-finite</a>  <a href="field_4.html#NM4" title="FIELD_4:NM.4">FieldExtension</a> of <font color="Maroon" title="c1">F</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">BE</font> being   <a href="vectsp_7.html#NM1" title="VECTSP_7:NM.1">Basis</a> of <span class="p1">(<span class="default"><a href="field_4.html#K2" title="FIELD_4:func.2">VecSp</a> (<font color="Maroon" title="c2">E</font>,<font color="Maroon" title="c1">F</font>)</span>)</span><br/>  for <font color="Olive" title="b2">BK</font> being   <a href="vectsp_7.html#NM1" title="VECTSP_7:NM.1">Basis</a> of <span class="p1">(<span class="default"><a href="field_4.html#K2" title="FIELD_4:func.2">VecSp</a> (<font color="Maroon" title="c3">K</font>,<font color="Maroon" title="c2">E</font>)</span>)</span><br/>  for <font color="Olive" title="b3">l</font> being    <a href="vectsp_6.html#M2" title="VECTSP_6:mode.2">Linear_Combination</a> of  <a href="field_7.html#K7" title="FIELD_7:func.7">Base</a> (<font color="Olive" title="b1">BE</font>,<font color="Olive" title="b2">BK</font>) holds   <a href="field_7.html#K10" title="FIELD_7:func.10">lift</a> (<span class="p1">(<span class="default"><a href="field_7.html#K9" title="FIELD_7:func.9">down</a> <font color="Olive" title="b3">l</font></span>)</span>,<font color="Olive" title="b1">BE</font>) <a href="vectsp_6.html#R1" title="VECTSP_6:pred.1">=</a> <font color="Olive" title="b3">l</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">BE</font> be   <a href="vectsp_7.html#NM1" title="VECTSP_7:NM.1">Basis</a> of <span class="p1">(<span class="default"><a href="field_4.html#K2" title="FIELD_4:func.2">VecSp</a> (<font color="Maroon" title="c2">E</font>,<font color="Maroon" title="c1">F</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">BK</font> being   <a href="vectsp_7.html#NM1" title="VECTSP_7:NM.1">Basis</a> of <span class="p1">(<span class="default"><a href="field_4.html#K2" title="FIELD_4:func.2">VecSp</a> (<font color="Maroon" title="c3">K</font>,<font color="Maroon" title="c2">E</font>)</span>)</span><br/>  for <font color="Olive" title="b2">l</font> being    <a href="vectsp_6.html#M2" title="VECTSP_6:mode.2">Linear_Combination</a> of  <a href="field_7.html#K7" title="FIELD_7:func.7">Base</a> (<font color="Maroon" title="c4">BE</font>,<font color="Olive" title="b1">BK</font>) holds   <a href="field_7.html#K10" title="FIELD_7:func.10">lift</a> (<span class="p1">(<span class="default"><a href="field_7.html#K9" title="FIELD_7:func.9">down</a> <font color="Olive" title="b2">l</font></span>)</span>,<font color="Maroon" title="c4">BE</font>) <a href="vectsp_6.html#R1" title="VECTSP_6:pred.1">=</a> <font color="Olive" title="b2">l</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">BK</font> be   <a href="vectsp_7.html#NM1" title="VECTSP_7:NM.1">Basis</a> of <span class="p1">(<span class="default"><a href="field_4.html#K2" title="FIELD_4:func.2">VecSp</a> (<font color="Maroon" title="c3">K</font>,<font color="Maroon" title="c2">E</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">l</font> being    <a href="vectsp_6.html#M2" title="VECTSP_6:mode.2">Linear_Combination</a> of  <a href="field_7.html#K7" title="FIELD_7:func.7">Base</a> (<font color="Maroon" title="c4">BE</font>,<font color="Maroon" title="c5">BK</font>) holds   <a href="field_7.html#K10" title="FIELD_7:func.10">lift</a> (<span class="p1">(<span class="default"><a href="field_7.html#K9" title="FIELD_7:func.9">down</a> <font color="Olive" title="b1">l</font></span>)</span>,<font color="Maroon" title="c4">BE</font>) <a href="vectsp_6.html#R1" title="VECTSP_6:pred.1">=</a> <font color="Olive" title="b1">l</font></span><br/><span class="kw">let </span><font color="Maroon" title="c6">l</font> be    <a href="vectsp_6.html#M2" title="VECTSP_6:mode.2">Linear_Combination</a> of  <a href="field_7.html#K7" title="FIELD_7:func.7">Base</a> (<font color="Maroon" title="c4">BE</font>,<font color="Maroon" title="c5">BK</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">  <a href="field_7.html#K10" title="FIELD_7:func.10">lift</a> (<span class="p1">(<span class="default"><a href="field_7.html#K9" title="FIELD_7:func.9">down</a> <font color="Maroon" title="c6">l</font></span>)</span>,<font color="Maroon" title="c4">BE</font>) <a href="vectsp_6.html#R1" title="VECTSP_6:pred.1">=</a> <font color="Maroon" title="c6">l</font></span><br/>











<a NAME="E1:58"/><span class="lab"><font color="Green" title="E29">H4</font></span>: 
 <a href="vectsp_6.html#K1" title="VECTSP_6:func.1">Carrier</a> <font color="Maroon" title="c6">l</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="field_7.html#K7" title="FIELD_7:func.7">Base</a> (<font color="Maroon" title="c4">BE</font>,<font color="Maroon" title="c5">BK</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_6.html#D4" onmouseover="rs('vectsp_6/D4')" onmouseout="rh()">VECTSP_6:def 4</a></span>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="58_1"><span class="kw">now </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">o</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="field_4.html#K2" title="FIELD_4:func.2">VecSp</a> (<font color="Maroon" title="c3">K</font>,<font color="Maroon" title="c1">F</font>)</span>)</span> holds <br/><font color="Maroon" title="c6">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="field_7.html#K10" title="FIELD_7:func.10">lift</a> (<span class="p2">(<span class="default"><a href="field_7.html#K9" title="FIELD_7:func.9">down</a> <font color="Maroon" title="c6">l</font></span>)</span>,<font color="Maroon" title="c4">BE</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">o</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">o</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="c7">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="field_4.html#K2" title="FIELD_4:func.2">VecSp</a> (<font color="Maroon" title="c3">K</font>,<font color="Maroon" title="c1">F</font>)</span>)</span> implies <font color="Maroon" title="c6">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="field_7.html#K10" title="FIELD_7:func.10">lift</a> (<span class="p2">(<span class="default"><a href="field_7.html#K9" title="FIELD_7:func.9">down</a> <font color="Maroon" title="c6">l</font></span>)</span>,<font color="Maroon" title="c4">BE</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> )</span><br/><span class="kw">assume </span><a NAME="E1:58_1"/><span class="lab"><font color="Green" title="E30">AS</font></span>: 
<font color="Maroon" title="c7">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="field_4.html#K2" title="FIELD_4:func.2">VecSp</a> (<font color="Maroon" title="c3">K</font>,<font color="Maroon" title="c1">F</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="c6">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="field_7.html#K10" title="FIELD_7:func.10">lift</a> (<span class="p2">(<span class="default"><a href="field_7.html#K9" title="FIELD_7:func.9">down</a> <font color="Maroon" title="c6">l</font></span>)</span>,<font color="Maroon" title="c4">BE</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c8">c</font> = <font color="Maroon" title="c7">o</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">K</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="field_4.html#D6" onmouseover="rs('field_4/D6')" onmouseout="rh()">FIELD_4:def 6</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c9">cV</font> = <font color="Maroon" title="c7">o</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="field_4.html#K2" title="FIELD_4:func.2">VecSp</a> (<font color="Maroon" title="c3">K</font>,<font color="Maroon" title="c1">F</font>)</span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:58_1"><span class="lab"><font color="Green" title="E30">AS</font></span></a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:58_1_1"/>
( <font color="Maroon" title="c8">c</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="field_7.html#K7" title="FIELD_7:func.7">Base</a> (<font color="Maroon" title="c4">BE</font>,<font color="Maroon" title="c5">BK</font>) or  not <font color="Maroon" title="c8">c</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="field_7.html#K7" title="FIELD_7:func.7">Base</a> (<font color="Maroon" title="c4">BE</font>,<font color="Maroon" title="c5">BK</font>) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:58_1_1_1"/><span class="lab"><font color="Green" title="E31">AS</font></span>: 
<font color="Maroon" title="c8">c</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="field_7.html#K7" title="FIELD_7:func.7">Base</a> (<font color="Maroon" title="c4">BE</font>,<font color="Maroon" title="c5">BK</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">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="field_7.html#K10" title="FIELD_7:func.10">lift</a> (<span class="p2">(<span class="default"><a href="field_7.html#K9" title="FIELD_7:func.9">down</a> <font color="Maroon" title="c6">l</font></span>)</span>,<font color="Maroon" title="c4">BE</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c10">a</font>, <font color="Maroon" title="c11">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">K</font><span class="kw"> such that </span><br/><a NAME="E3:58_1_1_1"/><span class="lab"><font color="Green" title="E32">A</font></span>: 
( <font color="Maroon" title="c8">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">b</font> &amp; <font color="Maroon" title="c10">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">BE</font> &amp; <font color="Maroon" title="c11">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c5">BK</font> )
 ;<br/><a NAME="E4:58_1_1_1"/><span class="lab"><font color="Green" title="E33">B</font></span>: 
<span class="p1">(<span class="default"><a href="field_7.html#K9" title="FIELD_7:func.9">down</a> <font color="Maroon" title="c6">l</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_6.html#K4" title="VECTSP_6:func.4">Sum</a> <span class="p1">(<span class="default"><a href="field_7.html#K8" title="FIELD_7:func.8">down</a> (<font color="Maroon" title="c6">l</font>,<font color="Maroon" title="c11">b</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:58_1_1_1"><span class="lab"><font color="Green" title="E32">A</font></span></a>, <a class="ref" href="field_7.html#D9" target="_self" onmouseover="rs('field_7/D9')" onmouseout="rh()">down2</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c12">l2</font> being    <a href="vectsp_6.html#M2" title="VECTSP_6:mode.2">Linear_Combination</a> of <font color="Maroon" title="c4">BE</font><span class="kw"> such that </span><br/><a NAME="E6:58_1_1_1"/><span class="lab"><font color="Green" title="E34">D</font></span>: 
(  <a href="vectsp_6.html#K4" title="VECTSP_6:func.4">Sum</a> <font color="Maroon" title="c12">l2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="field_7.html#K9" title="FIELD_7:func.9">down</a> <font color="Maroon" title="c6">l</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">b</font> &amp; (  for <font color="Olive" title="b1">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">K</font>  st <font color="Olive" title="b1">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c4">BE</font> &amp; <font color="Olive" title="b1">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="field_7.html#K7" title="FIELD_7:func.7">Base</a> (<font color="Maroon" title="c4">BE</font>,<font color="Maroon" title="c5">BK</font>) holds <br/><span class="p1">(<span class="default"><a href="field_7.html#K10" title="FIELD_7:func.10">lift</a> (<span class="p2">(<span class="default"><a href="field_7.html#K9" title="FIELD_7:func.9">down</a> <font color="Maroon" title="c6">l</font></span>)</span>,<font color="Maroon" title="c4">BE</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">l2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">a</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:58_1_1_1"><span class="lab"><font color="Green" title="E32">A</font></span></a>, <a class="ref" href="field_7.html#D10" target="_self" onmouseover="rs('field_7/D10')" onmouseout="rh()">lif</a></span>;<br/><a NAME="E7:58_1_1_1"/>
<font color="Maroon" title="c12">l2</font> <a href="vectsp_6.html#R1" title="VECTSP_6:pred.1">=</a>  <a href="field_7.html#K8" title="FIELD_7:func.8">down</a> (<font color="Maroon" title="c6">l</font>,<font color="Maroon" title="c11">b</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:58_1_1_1"><span class="lab"><font color="Green" title="E34">D</font></span></a>, <a class="txt" href="#E4:58_1_1_1"><span class="lab"><font color="Green" title="E33">B</font></span></a>, <a class="ref" href="field_7.html#T6" target="_self" onmouseover="rs('field_7/T6')" onmouseout="rh()">ZMODUL033</a></span>;<br/><span class="kw">then </span><span class="p1">(<span class="default"><a href="field_7.html#K10" title="FIELD_7:func.10">lift</a> (<span class="p2">(<span class="default"><a href="field_7.html#K9" title="FIELD_7:func.9">down</a> <font color="Maroon" title="c6">l</font></span>)</span>,<font color="Maroon" title="c4">BE</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">b</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="field_7.html#K8" title="FIELD_7:func.8">down</a> (<font color="Maroon" title="c6">l</font>,<font color="Maroon" title="c11">b</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">a</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:58_1_1_1"><span class="lab"><font color="Green" title="E32">A</font></span></a>, <a class="txt" href="#E6:58_1_1_1"><span class="lab"><font color="Green" title="E34">D</font></span></a>, <a class="txt" href="#E1:58_1_1_1"><span class="lab"><font color="Green" title="E31">AS</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c6">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c11">b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:58_1_1_1"><span class="lab"><font color="Green" title="E32">A</font></span></a>, <a class="ref" href="field_7.html#D8" target="_self" onmouseover="rs('field_7/D8')" onmouseout="rh()">down1</a></span>
;<br/><span class="kw">hence </span><a NAME="E9:58_1_1_1"/>
<font color="Maroon" title="c6">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="field_7.html#K10" title="FIELD_7:func.10">lift</a> (<span class="p2">(<span class="default"><a href="field_7.html#K9" title="FIELD_7:func.9">down</a> <font color="Maroon" title="c6">l</font></span>)</span>,<font color="Maroon" title="c4">BE</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">o</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:58_1_1_1"><span class="lab"><font color="Green" title="E32">A</font></span></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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:58_1_1_2"/><span class="lab"><font color="Green" title="E31">X</font></span>: 
 not <font color="Maroon" title="c8">c</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="field_7.html#K7" title="FIELD_7:func.7">Base</a> (<font color="Maroon" title="c4">BE</font>,<font color="Maroon" title="c5">BK</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">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="field_7.html#K10" title="FIELD_7:func.10">lift</a> (<span class="p2">(<span class="default"><a href="field_7.html#K9" title="FIELD_7:func.9">down</a> <font color="Maroon" title="c6">l</font></span>)</span>,<font color="Maroon" title="c4">BE</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font></span><br/><div class="add"><a NAME="E2:58_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A</font></span>: 
<font color="Maroon" title="c6">l</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">cV</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:58"><span class="lab"><font color="Green" title="E29">H4</font></span></a>, <a class="ref" href="vectsp_6.html#T2" onmouseover="rs('vectsp_6/T2')" onmouseout="rh()">VECTSP_6:2</a></span>;<br/><a NAME="E3:58_1_1_2"/>
 <a href="vectsp_6.html#K1" title="VECTSP_6:func.1">Carrier</a> <span class="p1">(<span class="default"><a href="field_7.html#K10" title="FIELD_7:func.10">lift</a> (<span class="p2">(<span class="default"><a href="field_7.html#K9" title="FIELD_7:func.9">down</a> <font color="Maroon" title="c6">l</font></span>)</span>,<font color="Maroon" title="c4">BE</font>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="field_7.html#K7" title="FIELD_7:func.7">Base</a> (<font color="Maroon" title="c4">BE</font>,<font color="Maroon" title="c5">BK</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_6.html#D4" onmouseover="rs('vectsp_6/D4')" onmouseout="rh()">VECTSP_6:def 4</a></span>;<br/><span class="kw">hence </span><a NAME="E4:58_1_1_2"/>
<font color="Maroon" title="c6">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="field_7.html#K10" title="FIELD_7:func.10">lift</a> (<span class="p2">(<span class="default"><a href="field_7.html#K9" title="FIELD_7:func.9">down</a> <font color="Maroon" title="c6">l</font></span>)</span>,<font color="Maroon" title="c4">BE</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">o</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:58_1_1_2"><span class="lab"><font color="Green" title="E32">A</font></span></a>, <a class="txt" href="#E1:58_1_1_2"><span class="lab"><font color="Green" title="E31">X</font></span></a>, <a class="ref" href="vectsp_6.html#T2" onmouseover="rs('vectsp_6/T2')" onmouseout="rh()">VECTSP_6:2</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></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:58"/>
 <a href="field_7.html#K10" title="FIELD_7:func.10">lift</a> (<span class="p1">(<span class="default"><a href="field_7.html#K9" title="FIELD_7:func.9">down</a> <font color="Maroon" title="c6">l</font></span>)</span>,<font color="Maroon" title="c4">BE</font>) <a href="vectsp_6.html#R1" title="VECTSP_6:pred.1">=</a> <font color="Maroon" title="c6">l</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"> verum</span><br/>


</div>
