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<b>let </b><font color="Maroon" title="c5">N1</font>, <font color="Maroon" title="c6">N2</font> be    <a href="msalimit.html#M2" title="MSALIMIT:mode.2">Binding</a> of <font color="Maroon" title="c3">OAF</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:9_1_2"/><i><font color="Green" title="E7">A35</font></i>: 
for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">P</font>  st <font color="Olive" title="b1">i</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Olive" title="b2">j</font> holds <br/><font color="Maroon" title="c5">N1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b2">j</font>,<font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_lang.html#K1" title="CQC_LANG:func.1">IFEQ</a> <font color="Olive" title="b2">j</font>,<font color="Olive" title="b1">i</font>,<span class="p1">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c3">OAF</font> <a href="pralg_2.html#K6" title="PRALG_2:func.6">.</a> <font color="Olive" title="b1">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msalimit.html#K1" title="MSALIMIT:func.1">bind</a> <font color="Maroon" title="c4">B</font>,<font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font></span>)</span> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <span class="p2">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p3">(<span class="default"><font color="Maroon" title="c3">OAF</font> <a href="pralg_2.html#K6" title="PRALG_2:func.6">.</a> <font color="Olive" title="b1">i</font></span>)</span></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E2:9_1_2"/><i><font color="Green" title="E8">A36</font></i>: 
for <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">P</font>  st <font color="Olive" title="b1">i</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Olive" title="b2">j</font> holds <br/><font color="Maroon" title="c6">N2</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b2">j</font>,<font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_lang.html#K1" title="CQC_LANG:func.1">IFEQ</a> <font color="Olive" title="b2">j</font>,<font color="Olive" title="b1">i</font>,<span class="p1">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c3">OAF</font> <a href="pralg_2.html#K6" title="PRALG_2:func.6">.</a> <font color="Olive" title="b1">i</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msalimit.html#K1" title="MSALIMIT:func.1">bind</a> <font color="Maroon" title="c4">B</font>,<font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font></span>)</span> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <span class="p2">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p3">(<span class="default"><font color="Maroon" title="c3">OAF</font> <a href="pralg_2.html#K6" title="PRALG_2:func.6">.</a> <font color="Olive" title="b1">i</font></span>)</span></span>)</span></span>)</span>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">ij</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:9_1_2_1"/><i><font color="Green" title="E9">A37</font></i>: 
<font color="Maroon" title="c7">ij</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">P</font>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c8">i2</font> = <font color="Maroon" title="c7">ij</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> , <font color="Maroon" title="c9">i1</font> = <font color="Maroon" title="c7">ij</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">P</font> <b>by </b><i><a class="ref" href="mcart_1.html#T10" title="MCART_1:th.10">MCART_1:10</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c10">i1</font> = <font color="Maroon" title="c9">i1</font>, <font color="Maroon" title="c11">i2</font> = <font color="Maroon" title="c8">i2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">P</font> ;<br/><a NAME="E4:9_1_2_1"/><i><font color="Green" title="E10">A38</font></i>: 
<font color="Maroon" title="c7">ij</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">ij</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c7">ij</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> </span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>by </b><i><a class="txt" href="msalimit.html#E1:9_1_2_1"><i><font color="Green" title="E9">A37</font></i></a>, <a class="ref" href="mcart_1.html#T23" title="MCART_1:th.23">MCART_1:23</a></i>;<br/><a NAME="E5:9_1_2_1"/><b>then </b><i><font color="Green" title="E11">A39</font></i>: 
<font color="Maroon" title="c11">i2</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c10">i1</font>
 <b>by </b><i><a class="txt" href="msalimit.html#E1:9_1_2_1"><i><font color="Green" title="E9">A37</font></i></a>, <a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></i>;<br/><a NAME="E6:9_1_2_1"/>
<font color="Maroon" title="c5">N1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">ij</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">N1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c11">i2</font>,<font color="Maroon" title="c10">i1</font>
 <b>by </b><i><a class="txt" href="msalimit.html#E4:9_1_2_1"><i><font color="Green" title="E10">A38</font></i></a></i>;<br/><a NAME="E7:9_1_2_1"/><b>then </b><i><font color="Green" title="E12">A40</font></i>: 
<font color="Maroon" title="c5">N1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">ij</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_lang.html#K1" title="CQC_LANG:func.1">IFEQ</a> <font color="Maroon" title="c11">i2</font>,<font color="Maroon" title="c10">i1</font>,<span class="p1">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c3">OAF</font> <a href="pralg_2.html#K6" title="PRALG_2:func.6">.</a> <font color="Maroon" title="c10">i1</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msalimit.html#K1" title="MSALIMIT:func.1">bind</a> <font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c10">i1</font>,<font color="Maroon" title="c11">i2</font></span>)</span> <a href="msualg_3.html#K3" title="MSUALG_3:func.3">**</a> <span class="p2">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p3">(<span class="default"><font color="Maroon" title="c3">OAF</font> <a href="pralg_2.html#K6" title="PRALG_2:func.6">.</a> <font color="Maroon" title="c10">i1</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="msalimit.html#E1:9_1_2"><i><font color="Green" title="E7">A35</font></i></a>, <a class="txt" href="msalimit.html#E5:9_1_2_1"><i><font color="Green" title="E11">A39</font></i></a></i>;<br/><a NAME="E8:9_1_2_1"/>
<font color="Maroon" title="c6">N2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">ij</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">N2</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c11">i2</font>,<font color="Maroon" title="c10">i1</font>
 <b>by </b><i><a class="txt" href="msalimit.html#E4:9_1_2_1"><i><font color="Green" title="E10">A38</font></i></a></i>;<br/><b>hence </b><a NAME="E9:9_1_2_1"/>
<font color="Maroon" title="c5">N1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">ij</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">N2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">ij</font>
 <b>by </b><i><a class="txt" href="msalimit.html#E2:9_1_2"><i><font color="Green" title="E8">A36</font></i></a>, <a class="txt" href="msalimit.html#E5:9_1_2_1"><i><font color="Green" title="E11">A39</font></i></a>, <a class="txt" href="msalimit.html#E7:9_1_2_1"><i><font color="Green" title="E12">A40</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:9_1_2"/>
<font color="Maroon" title="c5">N1</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c6">N2</font>
 <b>by </b><i><a class="ref" href="pboole.html#T3" title="PBOOLE:th.3">PBOOLE:3</a></i>;<br/>


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