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<span class="kw">let </span><font color="Maroon" title="c1">T</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">S</font> being non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a>   <a href="yellow_0.html#M1" title="YELLOW_0:mode.1">SubRelStr</a> of <font color="Maroon" title="c1">T</font><br/> for <font color="Olive" title="b2">X</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">S</font> holds <br/> ( <font color="Olive" title="b1">S</font> <a href="yellow16.html#R6" title="YELLOW16:pred.6">inherits_inf_of</a> <font color="Olive" title="b2">X</font>,<font color="Maroon" title="c1">T</font> iff (  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <font color="Olive" title="b2">X</font>,<font color="Maroon" title="c1">T</font> implies (  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <font color="Olive" title="b2">X</font>,<font color="Olive" title="b1">S</font> &amp;  <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <font color="Olive" title="b2">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <font color="Olive" title="b2">X</font>,<font color="Maroon" title="c1">T</font> ) ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">S</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a>   <a href="yellow_0.html#M1" title="YELLOW_0:mode.1">SubRelStr</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">X</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">S</font> holds <br/> ( <font color="Maroon" title="c2">S</font> <a href="yellow16.html#R6" title="YELLOW16:pred.6">inherits_inf_of</a> <font color="Olive" title="b1">X</font>,<font color="Maroon" title="c1">T</font> iff (  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <font color="Olive" title="b1">X</font>,<font color="Maroon" title="c1">T</font> implies (  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <font color="Olive" title="b1">X</font>,<font color="Maroon" title="c2">S</font> &amp;  <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <font color="Olive" title="b1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <font color="Olive" title="b1">X</font>,<font color="Maroon" title="c1">T</font> ) ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">X</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">S</font> <a href="yellow16.html#R6" title="YELLOW16:pred.6">inherits_inf_of</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">T</font> iff (  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">T</font> implies (  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c2">S</font> &amp;  <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <font color="Maroon" title="c3">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">T</font> ) ) )</span><br/>





<div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( (  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">T</font> implies (  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c2">S</font> &amp;  <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <font color="Maroon" title="c3">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">T</font> ) ) implies <font color="Maroon" title="c2">S</font> <a href="yellow16.html#R6" title="YELLOW16:pred.6">inherits_inf_of</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">T</font> )</span>
<div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:57_1"/><span class="lab"><font color="Green" title="E39">A1</font></span>: 
<font color="Maroon" title="c2">S</font> <a href="yellow16.html#R6" title="YELLOW16:pred.6">inherits_inf_of</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">T</font>
 <span class="kw">and </span><br/><a NAME="E2:57_1"/><span class="lab"><font color="Green" title="E40">A2</font></span>: 
 <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">T</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c2">S</font> &amp;  <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <font color="Maroon" title="c3">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">T</font> )</span><br/><a NAME="E3:57_1"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">T</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 <font color="Maroon" title="c2">S</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:57_1"><span class="lab"><font color="Green" title="E39">A1</font></span></a>, <a class="txt" href="#E2:57_1"><span class="lab"><font color="Green" title="E40">A2</font></span></a>, <a class="ref" href="yellow16.html#D7" target="_self" title="YELLOW16:def.7">Def7</a></span>;<br/><span class="kw">hence </span><a NAME="E4:57_1"/>
(  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c2">S</font> &amp;  <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <font color="Maroon" title="c3">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">T</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:57_1"><span class="lab"><font color="Green" title="E40">A2</font></span></a>, <a class="ref" href="yellow_0.html#T64" title="YELLOW_0:th.64">YELLOW_0:64</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E2:57"/><span class="lab"><font color="Green" title="E39">A3</font></span>: 
(  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">T</font> implies (  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c2">S</font> &amp;  <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <font color="Maroon" title="c3">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">T</font> ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">S</font> <a href="yellow16.html#R6" title="YELLOW16:pred.6">inherits_inf_of</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">T</font></span><br/>

<span class="kw">assume </span><a NAME="E3:57"/>
 <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">T</font>
 ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="yellow16.html#D7" target="_self" title="YELLOW16:def.7">YELLOW16:def 7</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">T</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 <font color="Maroon" title="c2">S</font></span><br/>

<span class="kw">hence </span><a NAME="E4:57"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">T</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 <font color="Maroon" title="c2">S</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:57"><span class="lab"><font color="Green" title="E39">A3</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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