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<span class="kw">let </span><font color="Maroon" title="c1">i</font>, <font color="Maroon" title="c2">j</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</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">N</font> being non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <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>   st <font color="Maroon" title="c1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">j</font> holds <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#V4" title="AMI_1:attr.4">halting</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">steady-programmed</a>   <a href="ami_1.html#V8" title="AMI_1:attr.8">definite</a>   <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Olive" title="b1">N</font><br/> for <font color="Olive" title="b3">P</font> being the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <font color="Olive">b<sub>2</sub></font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <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="b2">S</font>  st <font color="Olive" title="b3">P</font> <a href="ami_1.html#R3" title="AMI_1:pred.3">halts_at</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Olive" title="b3">P</font>,<font color="Olive" title="b4">s</font>,<font color="Maroon" title="c1">i</font></span>)</span> holds <br/> <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Olive" title="b3">P</font>,<font color="Olive" title="b4">s</font>,<font color="Maroon" title="c2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Olive" title="b3">P</font>,<font color="Olive" title="b4">s</font>,<font color="Maroon" title="c1">i</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">N</font> be  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">j</font> implies 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#V4" title="AMI_1:attr.4">halting</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">steady-programmed</a>   <a href="ami_1.html#V8" title="AMI_1:attr.8">definite</a>   <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c3">N</font><br/> for <font color="Olive" title="b2">P</font> being the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <font color="Olive">b<sub>1</sub></font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <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="Olive" title="b1">S</font>  st <font color="Olive" title="b2">P</font> <a href="ami_1.html#R3" title="AMI_1:pred.3">halts_at</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Olive" title="b2">P</font>,<font color="Olive" title="b3">s</font>,<font color="Maroon" title="c1">i</font></span>)</span> holds <br/> <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Olive" title="b2">P</font>,<font color="Olive" title="b3">s</font>,<font color="Maroon" title="c2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Olive" title="b2">P</font>,<font color="Olive" title="b3">s</font>,<font color="Maroon" title="c1">i</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:180"/><span class="lab"><font color="Green" title="E49">A1</font></span>: 
<font color="Maroon" title="c1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">j</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">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#V4" title="AMI_1:attr.4">halting</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">steady-programmed</a>   <a href="ami_1.html#V8" title="AMI_1:attr.8">definite</a>   <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c3">N</font><br/> for <font color="Olive" title="b2">P</font> being the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <font color="Olive">b<sub>1</sub></font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <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="Olive" title="b1">S</font>  st <font color="Olive" title="b2">P</font> <a href="ami_1.html#R3" title="AMI_1:pred.3">halts_at</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Olive" title="b2">P</font>,<font color="Olive" title="b3">s</font>,<font color="Maroon" title="c1">i</font></span>)</span> holds <br/> <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Olive" title="b2">P</font>,<font color="Olive" title="b3">s</font>,<font color="Maroon" title="c2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Olive" title="b2">P</font>,<font color="Olive" title="b3">s</font>,<font color="Maroon" title="c1">i</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c4">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#V4" title="AMI_1:attr.4">halting</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">steady-programmed</a>   <a href="ami_1.html#V8" title="AMI_1:attr.8">definite</a>   <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of <font color="Maroon" title="c3">N</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">P</font> being the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <font color="Maroon" title="c4">S</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <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="c4">S</font>  st <font color="Olive" title="b1">P</font> <a href="ami_1.html#R3" title="AMI_1:pred.3">halts_at</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Olive" title="b1">P</font>,<font color="Olive" title="b2">s</font>,<font color="Maroon" title="c1">i</font></span>)</span> holds <br/> <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Olive" title="b1">P</font>,<font color="Olive" title="b2">s</font>,<font color="Maroon" title="c2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Olive" title="b1">P</font>,<font color="Olive" title="b2">s</font>,<font color="Maroon" title="c1">i</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">P</font> be  the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <font color="Maroon" title="c4">S</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</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  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <font color="Maroon" title="c4">S</font>  st <font color="Maroon" title="c5">P</font> <a href="ami_1.html#R3" title="AMI_1:pred.3">halts_at</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c5">P</font>,<font color="Olive" title="b1">s</font>,<font color="Maroon" title="c1">i</font></span>)</span> holds <br/> <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c5">P</font>,<font color="Olive" title="b1">s</font>,<font color="Maroon" title="c2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c5">P</font>,<font color="Olive" title="b1">s</font>,<font color="Maroon" title="c1">i</font></span><br/><span class="kw">let </span><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="c4">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="c5">P</font> <a href="ami_1.html#R3" title="AMI_1:pred.3">halts_at</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c1">i</font></span>)</span> implies  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c1">i</font> )</span><br/>





<span class="kw">assume </span><a NAME="E2:180"/><span class="lab"><font color="Green" title="E50">A2</font></span>: 
<font color="Maroon" title="c5">P</font> <a href="ami_1.html#R3" title="AMI_1:pred.3">halts_at</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c1">i</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c1">i</font></span><br/>

<a NAME="E3:180"/><span class="kw">then </span>
<font color="Maroon" title="c5">P</font> <a href="ami_1.html#R3" title="AMI_1:pred.3">halts_at</a>  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c2">j</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:180"><span class="lab"><font color="Green" title="E49">A1</font></span></a>, <a class="ref" href="ami_1.html#T88" target="_self" title="AMI_1:th.88">Th88</a></span>;<br/>
<span class="kw">hence </span> <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c2">j</font> = 
 <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c6">s</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#T87" target="_self" title="AMI_1:th.87">Th87</a></span>
<br/>.= 
 <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c6">s</font>,<font color="Maroon" title="c1">i</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:180"><span class="lab"><font color="Green" title="E50">A2</font></span></a>, <a class="ref" href="ami_1.html#T87" target="_self" title="AMI_1:th.87">Th87</a></span>
;<br/> <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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