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<b>let </b><font color="Maroon" title="c1">IL</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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">N</font> being <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">with_non-empty_elements</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/> for <font color="Olive" title="b2">S</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="ami_1.html#V2" title="AMI_1:attr.2">stored-program</a> <a href="ami_1.html#V5" title="AMI_1:attr.5">IC-Ins-separated</a> <a href="ami_1.html#V7" title="AMI_1:attr.7">definite</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">IL</font>,<font color="Olive" title="b1">N</font><br/> for <font color="Olive" title="b3">p</font> being  <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <font color="Olive" title="b2">S</font><br/> for <font color="Olive" title="b4">l</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">IL</font>  st <font color="Olive" title="b3">p</font> <a href="ami_1.html#R4" title="AMI_1:pred.4">starts_at</a> <font color="Olive" title="b4">l</font> holds <br/>for <font color="Olive" title="b5">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <font color="Olive" title="b2">S</font>  st <font color="Olive" title="b3">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b5">s</font> holds <br/><font color="Olive" title="b5">s</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">starts_at</a> <font color="Olive" title="b4">l</font></span><br/><b>let </b><font color="Maroon" title="c2">N</font> be  <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">with_non-empty_elements</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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">S</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="ami_1.html#V2" title="AMI_1:attr.2">stored-program</a> <a href="ami_1.html#V5" title="AMI_1:attr.5">IC-Ins-separated</a> <a href="ami_1.html#V7" title="AMI_1:attr.7">definite</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">IL</font>,<font color="Maroon" title="c2">N</font><br/> for <font color="Olive" title="b2">p</font> being  <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <font color="Olive" title="b1">S</font><br/> for <font color="Olive" title="b3">l</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">IL</font>  st <font color="Olive" title="b2">p</font> <a href="ami_1.html#R4" title="AMI_1:pred.4">starts_at</a> <font color="Olive" title="b3">l</font> holds <br/>for <font color="Olive" title="b4">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <font color="Olive" title="b1">S</font>  st <font color="Olive" title="b2">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b4">s</font> holds <br/><font color="Olive" title="b4">s</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">starts_at</a> <font color="Olive" title="b3">l</font></span><br/><b>let </b><font color="Maroon" title="c3">S</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="ami_1.html#V2" title="AMI_1:attr.2">stored-program</a> <a href="ami_1.html#V5" title="AMI_1:attr.5">IC-Ins-separated</a> <a href="ami_1.html#V7" title="AMI_1:attr.7">definite</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c1">IL</font>,<font color="Maroon" title="c2">N</font>; <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">p</font> being  <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <font color="Maroon" title="c3">S</font><br/> for <font color="Olive" title="b2">l</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">IL</font>  st <font color="Olive" title="b1">p</font> <a href="ami_1.html#R4" title="AMI_1:pred.4">starts_at</a> <font color="Olive" title="b2">l</font> holds <br/>for <font color="Olive" title="b3">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <font color="Maroon" title="c3">S</font>  st <font color="Olive" title="b1">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">s</font> holds <br/><font color="Olive" title="b3">s</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">starts_at</a> <font color="Olive" title="b2">l</font></span><br/><b>let </b><font color="Maroon" title="c4">p</font> be   <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <font color="Maroon" title="c3">S</font>; <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">l</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">IL</font>  st <font color="Maroon" title="c4">p</font> <a href="ami_1.html#R4" title="AMI_1:pred.4">starts_at</a> <font color="Olive" title="b1">l</font> holds <br/>for <font color="Olive" title="b2">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <font color="Maroon" title="c3">S</font>  st <font color="Maroon" title="c4">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">s</font> holds <br/><font color="Olive" title="b2">s</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">starts_at</a> <font color="Olive" title="b1">l</font></span><br/><b>let </b><font color="Maroon" title="c5">l</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">IL</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">p</font> <a href="ami_1.html#R4" title="AMI_1:pred.4">starts_at</a> <font color="Maroon" title="c5">l</font> implies for <font color="Olive" title="b1">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <font color="Maroon" title="c3">S</font>  st <font color="Maroon" title="c4">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">s</font> holds <br/><font color="Olive" title="b1">s</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">starts_at</a> <font color="Maroon" title="c5">l</font> )</span><br/>









<b>assume </b><a NAME="E1:139"/><i><font color="Green" title="E59">A1</font></i>: 
(  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c3">S</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">p</font> &amp;  <a href="ami_1.html#K29" title="AMI_1:func.29">IC</a> <font color="Maroon" title="c4">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">l</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D44" target="_self" title="AMI_1:def.44">AMI_1:def 44</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">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <font color="Maroon" title="c3">S</font>  st <font color="Maroon" title="c4">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">s</font> holds <br/><font color="Olive" title="b1">s</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">starts_at</a> <font color="Maroon" title="c5">l</font></span><br/>

<b>let </b><font color="Maroon" title="c6">s</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <font color="Maroon" title="c3">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">s</font> implies <font color="Maroon" title="c6">s</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">starts_at</a> <font color="Maroon" title="c5">l</font> )</span><br/>

<b>assume </b><a NAME="E2:139"/><i><font color="Green" title="E60">A2</font></i>: 
<font color="Maroon" title="c4">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">s</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">s</font> <a href="ami_1.html#R2" title="AMI_1:pred.2">starts_at</a> <font color="Maroon" title="c5">l</font></span><br/>

<b>thus </b> <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c6">s</font> = 
<font color="Maroon" title="c4">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <font color="Maroon" title="c3">S</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:139"><i><font color="Green" title="E59">A1</font></i></a>, <a class="txt" href="#E2:139"><i><font color="Green" title="E60">A2</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>
<br/>.= 
<font color="Maroon" title="c5">l</font>
<b>by </b><i><a class="txt" href="#E1:139"><i><font color="Green" title="E59">A1</font></i></a>, <a class="ref" href="ami_1.html#D43" target="_self" title="AMI_1:def.43">Def43</a></i>
; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D41" target="_self" title="AMI_1:def.41">AMI_1:def 41</a> <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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