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<b>let </b><font color="Maroon" title="c1">S1</font>, <font color="Maroon" title="c2">S2</font> be    <a href="incsp_1.html#L1" title="INCSP_1:struct.1">IncProjStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">F1</font>, <font color="Olive" title="b2">F2</font> being   <a href="combgras.html#L1" title="COMBGRAS:struct.1">IncProjMap</a> of <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font>  st  <a href="combgras.html#G1" title="COMBGRAS:aggr.1">IncProjMap</a>(# the <a href="combgras.html#U1" title="COMBGRAS:sel.1">point-map</a> of <font color="Olive" title="b1">F1</font>,the <a href="combgras.html#U2" title="COMBGRAS:sel.2">line-map</a> of <font color="Olive" title="b1">F1</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="combgras.html#G1" title="COMBGRAS:aggr.1">IncProjMap</a>(# the <a href="combgras.html#U1" title="COMBGRAS:sel.1">point-map</a> of <font color="Olive" title="b2">F2</font>,the <a href="combgras.html#U2" title="COMBGRAS:sel.2">line-map</a> of <font color="Olive" title="b2">F2</font> #) &amp; <font color="Olive" title="b1">F1</font> is <a href="combgras.html#V6" title="COMBGRAS:attr.6">incidence_preserving</a> holds <br/><font color="Olive" title="b2">F2</font> is <a href="combgras.html#V6" title="COMBGRAS:attr.6">incidence_preserving</a></span><br/><b>let </b><font color="Maroon" title="c3">F1</font>, <font color="Maroon" title="c4">F2</font> be    <a href="combgras.html#L1" title="COMBGRAS:struct.1">IncProjMap</a> of <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="combgras.html#G1" title="COMBGRAS:aggr.1">IncProjMap</a>(# the <a href="combgras.html#U1" title="COMBGRAS:sel.1">point-map</a> of <font color="Maroon" title="c3">F1</font>,the <a href="combgras.html#U2" title="COMBGRAS:sel.2">line-map</a> of <font color="Maroon" title="c3">F1</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="combgras.html#G1" title="COMBGRAS:aggr.1">IncProjMap</a>(# the <a href="combgras.html#U1" title="COMBGRAS:sel.1">point-map</a> of <font color="Maroon" title="c4">F2</font>,the <a href="combgras.html#U2" title="COMBGRAS:sel.2">line-map</a> of <font color="Maroon" title="c4">F2</font> #) &amp; <font color="Maroon" title="c3">F1</font> is <a href="combgras.html#V6" title="COMBGRAS:attr.6">incidence_preserving</a> implies <font color="Maroon" title="c4">F2</font> is <a href="combgras.html#V6" title="COMBGRAS:attr.6">incidence_preserving</a> )</span><br/>



<b>assume </b><a NAME="E1:27"/><i><font color="Green" title="E22">A1</font></i>: 
(  <a href="combgras.html#G1" title="COMBGRAS:aggr.1">IncProjMap</a>(# the <a href="combgras.html#U1" title="COMBGRAS:sel.1">point-map</a> of <font color="Maroon" title="c3">F1</font>,the <a href="combgras.html#U2" title="COMBGRAS:sel.2">line-map</a> of <font color="Maroon" title="c3">F1</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="combgras.html#G1" title="COMBGRAS:aggr.1">IncProjMap</a>(# the <a href="combgras.html#U1" title="COMBGRAS:sel.1">point-map</a> of <font color="Maroon" title="c4">F2</font>,the <a href="combgras.html#U2" title="COMBGRAS:sel.2">line-map</a> of <font color="Maroon" title="c4">F2</font> #) &amp; <font color="Maroon" title="c3">F1</font> is <a href="combgras.html#V6" title="COMBGRAS:attr.6">incidence_preserving</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">F2</font> is <a href="combgras.html#V6" title="COMBGRAS:attr.6">incidence_preserving</a></span><br/>

<b>let </b><font color="Maroon" title="c5">A1</font> be   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">S1</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="combgras.html#D8" target="_self" title="COMBGRAS:def.8">COMBGRAS:def 8</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">L1</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">S1</font> holds <br/> ( <font color="Maroon" title="c5">A1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">L1</font> iff <font color="Maroon" title="c4">F2</font> <a href="combgras.html#K2" title="COMBGRAS:func.2">.</a> <font color="Maroon" title="c5">A1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c4">F2</font> <a href="combgras.html#K3" title="COMBGRAS:func.3">.</a> <font color="Olive" title="b1">L1</font> )</span><br/><b>let </b><font color="Maroon" title="c6">L1</font> be   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">S1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">A1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c6">L1</font> iff <font color="Maroon" title="c4">F2</font> <a href="combgras.html#K2" title="COMBGRAS:func.2">.</a> <font color="Maroon" title="c5">A1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c4">F2</font> <a href="combgras.html#K3" title="COMBGRAS:func.3">.</a> <font color="Maroon" title="c6">L1</font> )</span><br/>



<a NAME="E2:27"/>
( <font color="Maroon" title="c4">F2</font> <a href="combgras.html#K2" title="COMBGRAS:func.2">.</a> <font color="Maroon" title="c5">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F1</font> <a href="combgras.html#K2" title="COMBGRAS:func.2">.</a> <font color="Maroon" title="c5">A1</font> &amp; <font color="Maroon" title="c4">F2</font> <a href="combgras.html#K3" title="COMBGRAS:func.3">.</a> <font color="Maroon" title="c6">L1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F1</font> <a href="combgras.html#K3" title="COMBGRAS:func.3">.</a> <font color="Maroon" title="c6">L1</font> )
 
<b>by </b><i><a class="txt" href="combgras.html#E1:27"><i><font color="Green" title="E22">A1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:27"/>
( <font color="Maroon" title="c5">A1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c6">L1</font> iff <font color="Maroon" title="c4">F2</font> <a href="combgras.html#K2" title="COMBGRAS:func.2">.</a> <font color="Maroon" title="c5">A1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c4">F2</font> <a href="combgras.html#K3" title="COMBGRAS:func.3">.</a> <font color="Maroon" title="c6">L1</font> )
 <b>by </b><i><a class="txt" href="combgras.html#E1:27"><i><font color="Green" title="E22">A1</font></i></a>, <a class="ref" href="combgras.html#D8" target="_self" title="COMBGRAS:def.8">Def8</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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