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<b>let </b><font color="Maroon" title="c1">T1</font>, <font color="Maroon" title="c2">T2</font> be    <a href="abcmiz_0.html#L2" title="ABCMIZ_0:struct.2">TA-structure</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="abcmiz_0.html#G2" title="ABCMIZ_0:aggr.2">TA-structure</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T1</font>,the <a href="abcmiz_0.html#U1" title="ABCMIZ_0:sel.1">adjectives</a> of <font color="Maroon" title="c1">T1</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">T1</font>,the <a href="abcmiz_0.html#U2" title="ABCMIZ_0:sel.2">non-op</a> of <font color="Maroon" title="c1">T1</font>,the <a href="abcmiz_0.html#U3" title="ABCMIZ_0:sel.3">adj-map</a> of <font color="Maroon" title="c1">T1</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_0.html#G2" title="ABCMIZ_0:aggr.2">TA-structure</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">T2</font>,the <a href="abcmiz_0.html#U1" title="ABCMIZ_0:sel.1">adjectives</a> of <font color="Maroon" title="c2">T2</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">T2</font>,the <a href="abcmiz_0.html#U2" title="ABCMIZ_0:sel.2">non-op</a> of <font color="Maroon" title="c2">T2</font>,the <a href="abcmiz_0.html#U3" title="ABCMIZ_0:sel.3">adj-map</a> of <font color="Maroon" title="c2">T2</font> #) implies for <font color="Olive" title="b1">a1</font> being  <a href="abcmiz_0.html#NM2" title="ABCMIZ_0:NM.2">adjective</a> of <font color="Maroon" title="c1">T1</font><br/> for <font color="Olive" title="b2">a2</font> being  <a href="abcmiz_0.html#NM2" title="ABCMIZ_0:NM.2">adjective</a> of <font color="Maroon" title="c2">T2</font>  st <font color="Olive" title="b1">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a2</font> holds <br/> <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Olive" title="b1">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Olive" title="b2">a2</font> )</span><br/>

<b>assume </b><a NAME="E1:35"/><i><font color="Green" title="E17">A1</font></i>: 
 <a href="abcmiz_0.html#G2" title="ABCMIZ_0:aggr.2">TA-structure</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T1</font>,the <a href="abcmiz_0.html#U1" title="ABCMIZ_0:sel.1">adjectives</a> of <font color="Maroon" title="c1">T1</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">T1</font>,the <a href="abcmiz_0.html#U2" title="ABCMIZ_0:sel.2">non-op</a> of <font color="Maroon" title="c1">T1</font>,the <a href="abcmiz_0.html#U3" title="ABCMIZ_0:sel.3">adj-map</a> of <font color="Maroon" title="c1">T1</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_0.html#G2" title="ABCMIZ_0:aggr.2">TA-structure</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">T2</font>,the <a href="abcmiz_0.html#U1" title="ABCMIZ_0:sel.1">adjectives</a> of <font color="Maroon" title="c2">T2</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">T2</font>,the <a href="abcmiz_0.html#U2" title="ABCMIZ_0:sel.2">non-op</a> of <font color="Maroon" title="c2">T2</font>,the <a href="abcmiz_0.html#U3" title="ABCMIZ_0:sel.3">adj-map</a> of <font color="Maroon" title="c2">T2</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">a1</font> being  <a href="abcmiz_0.html#NM2" title="ABCMIZ_0:NM.2">adjective</a> of <font color="Maroon" title="c1">T1</font><br/> for <font color="Olive" title="b2">a2</font> being  <a href="abcmiz_0.html#NM2" title="ABCMIZ_0:NM.2">adjective</a> of <font color="Maroon" title="c2">T2</font>  st <font color="Olive" title="b1">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a2</font> holds <br/> <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Olive" title="b1">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Olive" title="b2">a2</font></span><br/>

<b>let </b><font color="Maroon" title="c3">a1</font> be   <a href="abcmiz_0.html#NM2" title="ABCMIZ_0:NM.2">adjective</a> of <font color="Maroon" title="c1">T1</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">a2</font> being  <a href="abcmiz_0.html#NM2" title="ABCMIZ_0:NM.2">adjective</a> of <font color="Maroon" title="c2">T2</font>  st <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a2</font> holds <br/> <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Olive" title="b1">a2</font></span><br/><b>let </b><font color="Maroon" title="c4">a2</font> be   <a href="abcmiz_0.html#NM2" title="ABCMIZ_0:NM.2">adjective</a> of <font color="Maroon" title="c2">T2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a2</font> implies  <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c4">a2</font> )</span><br/>



<b>assume </b><a NAME="E2:35"/><i><font color="Green" title="E18">A2</font></i>: 
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c4">a2</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1"><b>now </b></a><div class="add"><b>thus </b><a NAME="E1:35_1"/>
 <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c3">a1</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">T2</font>
 <b>by </b><i><a class="txt" href="#E1:35"><i><font color="Green" title="E17">A1</font></i></a></i>; <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">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c3">a1</font> implies  ex <font color="Olive" title="b2">t2</font> being  <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c2">T2</font> st <br/>( <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">t2</font> &amp; <font color="Maroon" title="c4">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <font color="Olive" title="b2">t2</font> ) ) &amp; (  ex <font color="Olive" title="b2">t2</font> being  <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c2">T2</font> st <br/>( <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">t2</font> &amp; <font color="Maroon" title="c4">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <font color="Olive" title="b2">t2</font> ) implies <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c3">a1</font> ) )</span><br/><b>let </b><font color="Maroon" title="c5">x</font> be    <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"> ( ( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c3">a1</font> implies  ex <font color="Olive" title="b1">t2</font> being  <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c2">T2</font> st <br/>( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">t2</font> &amp; <font color="Maroon" title="c4">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <font color="Olive" title="b1">t2</font> ) ) &amp; (  ex <font color="Olive" title="b1">t2</font> being  <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c2">T2</font> st <br/>( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">t2</font> &amp; <font color="Maroon" title="c4">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <font color="Olive" title="b1">t2</font> ) implies <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c3">a1</font> ) )</span><br/><div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  ex <font color="Olive" title="b1">t2</font> being  <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c2">T2</font> st <br/>( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">t2</font> &amp; <font color="Maroon" title="c4">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <font color="Olive" title="b1">t2</font> ) implies <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c3">a1</font> )</span>
<div class="add"><b>assume </b><a NAME="E1:35_1_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c3">a1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">t2</font> being  <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c2">T2</font> st <br/>( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">t2</font> &amp; <font color="Maroon" title="c4">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <font color="Olive" title="b1">t2</font> )</span><br/><b>then consider </b><font color="Maroon" title="c6">t1</font> being   <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c1">T1</font><b> such that </b><br/><a NAME="E3:35_1_1"/><i><font color="Green" title="E19">A3</font></i>: 
( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">t1</font> &amp; <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <font color="Maroon" title="c6">t1</font> )
 <b>by </b><i><a class="ref" href="abcmiz_0.html#D12" target="_self" title="ABCMIZ_0:def.12">Def12</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c7">t2</font> = <font color="Maroon" title="c6">t1</font> as   <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c2">T2</font> <b>by </b><i><a class="txt" href="#E1:35"><i><font color="Green" title="E17">A1</font></i></a></i>;<br/><a NAME="E5:35_1_1"/>
 <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <font color="Maroon" title="c6">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <font color="Maroon" title="c7">t2</font>
 <b>by </b><i><a class="txt" href="#E1:35"><i><font color="Green" title="E17">A1</font></i></a></i>;<br/><b>hence </b><a NAME="E6:35_1_1"/>
 ex <font color="Olive" title="b1">t2</font> being  <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c2">T2</font> st <br/>( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">t2</font> &amp; <font color="Maroon" title="c4">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <font color="Olive" title="b1">t2</font> )
 <b>by </b><i><a class="txt" href="#E2:35"><i><font color="Green" title="E18">A2</font></i></a>, <a class="txt" href="#E3:35_1_1"><i><font color="Green" title="E19">A3</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div>
<b>end;</b></div><b>given </b><font color="Maroon" title="c6">t2</font> being   <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c2">T2</font><b> such that </b><a NAME="E4:35_1"/><i><font color="Green" title="E19">A4</font></i>: 
( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">t2</font> &amp; <font color="Maroon" title="c4">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <font color="Maroon" title="c6">t2</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">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c3">a1</font></span><br/><b>reconsider </b><font color="Maroon" title="c7">t1</font> = <font color="Maroon" title="c6">t2</font> as   <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c1">T1</font> <b>by </b><i><a class="txt" href="#E1:35"><i><font color="Green" title="E17">A1</font></i></a></i>;<br/><a NAME="E6:35_1"/>
 <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <font color="Maroon" title="c7">t1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_0.html#K2" title="ABCMIZ_0:func.2">adjs</a> <font color="Maroon" title="c6">t2</font>
 <b>by </b><i><a class="txt" href="#E1:35"><i><font color="Green" title="E17">A1</font></i></a></i>;<br/><b>hence </b><a NAME="E7:35_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c3">a1</font>
 <b>by </b><i><a class="txt" href="#E2:35"><i><font color="Green" title="E18">A2</font></i></a>, <a class="txt" href="#E4:35_1"><i><font color="Green" title="E19">A4</font></i></a>, <a class="ref" href="abcmiz_0.html#D12" target="_self" title="ABCMIZ_0:def.12">Def12</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:35"/>
 <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="abcmiz_0.html#K3" title="ABCMIZ_0:func.3">types</a> <font color="Maroon" title="c4">a2</font>
 <b>by </b><i><a class="ref" href="abcmiz_0.html#D12" target="_self" title="ABCMIZ_0:def.12">Def12</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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