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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">m1</font>, <font color="Olive" title="b2">m2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K20" title="COH_SP:func.20">MapsT</a> <font color="Maroon" title="c1">X</font>  st  <a href="coh_sp.html#K21" title="COH_SP:func.21">dom</a> <font color="Olive" title="b2">m2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K22" title="COH_SP:func.22">cod</a> <font color="Olive" title="b1">m1</font> holds <br/>( <span class="p1">(<span class="default"><font color="Olive" title="b2">m2</font> <a href="coh_sp.html#K24" title="COH_SP:func.24">*</a> <font color="Olive" title="b1">m1</font></span>)</span> <a href="xfamily.html#K2" title="XFAMILY:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">m2</font> <a href="xfamily.html#K2" title="XFAMILY:func.2">`2</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">m1</font> <a href="xfamily.html#K2" title="XFAMILY:func.2">`2</a></span>)</span> &amp;  <a href="coh_sp.html#K21" title="COH_SP:func.21">dom</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">m2</font> <a href="coh_sp.html#K24" title="COH_SP:func.24">*</a> <font color="Olive" title="b1">m1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K21" title="COH_SP:func.21">dom</a> <font color="Olive" title="b1">m1</font> &amp;  <a href="coh_sp.html#K22" title="COH_SP:func.22">cod</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">m2</font> <a href="coh_sp.html#K24" title="COH_SP:func.24">*</a> <font color="Olive" title="b1">m1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K22" title="COH_SP:func.22">cod</a> <font color="Olive" title="b2">m2</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">m1</font>, <font color="Maroon" title="c3">m2</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K20" title="COH_SP:func.20">MapsT</a> <font color="Maroon" title="c1">X</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="coh_sp.html#K21" title="COH_SP:func.21">dom</a> <font color="Maroon" title="c3">m2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K22" title="COH_SP:func.22">cod</a> <font color="Maroon" title="c2">m1</font> implies ( <span class="p1">(<span class="default"><font color="Maroon" title="c3">m2</font> <a href="coh_sp.html#K24" title="COH_SP:func.24">*</a> <font color="Maroon" title="c2">m1</font></span>)</span> <a href="xfamily.html#K2" title="XFAMILY:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">m2</font> <a href="xfamily.html#K2" title="XFAMILY:func.2">`2</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m1</font> <a href="xfamily.html#K2" title="XFAMILY:func.2">`2</a></span>)</span> &amp;  <a href="coh_sp.html#K21" title="COH_SP:func.21">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">m2</font> <a href="coh_sp.html#K24" title="COH_SP:func.24">*</a> <font color="Maroon" title="c2">m1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K21" title="COH_SP:func.21">dom</a> <font color="Maroon" title="c2">m1</font> &amp;  <a href="coh_sp.html#K22" title="COH_SP:func.22">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">m2</font> <a href="coh_sp.html#K24" title="COH_SP:func.24">*</a> <font color="Maroon" title="c2">m1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K22" title="COH_SP:func.22">cod</a> <font color="Maroon" title="c3">m2</font> ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:76"/>
 <a href="coh_sp.html#K21" title="COH_SP:func.21">dom</a> <font color="Maroon" title="c3">m2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K22" title="COH_SP:func.22">cod</a> <font color="Maroon" title="c2">m1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><font color="Maroon" title="c3">m2</font> <a href="coh_sp.html#K24" title="COH_SP:func.24">*</a> <font color="Maroon" title="c2">m1</font></span>)</span> <a href="xfamily.html#K2" title="XFAMILY:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">m2</font> <a href="xfamily.html#K2" title="XFAMILY:func.2">`2</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m1</font> <a href="xfamily.html#K2" title="XFAMILY:func.2">`2</a></span>)</span> &amp;  <a href="coh_sp.html#K21" title="COH_SP:func.21">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">m2</font> <a href="coh_sp.html#K24" title="COH_SP:func.24">*</a> <font color="Maroon" title="c2">m1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K21" title="COH_SP:func.21">dom</a> <font color="Maroon" title="c2">m1</font> &amp;  <a href="coh_sp.html#K22" title="COH_SP:func.22">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">m2</font> <a href="coh_sp.html#K24" title="COH_SP:func.24">*</a> <font color="Maroon" title="c2">m1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K22" title="COH_SP:func.22">cod</a> <font color="Maroon" title="c3">m2</font> )</span><br/>

<span class="kw">then </span><span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><a href="coh_sp.html#K21" title="COH_SP:func.21">dom</a> <font color="Maroon" title="c2">m1</font></span>)</span>,<span class="p3">(<span class="default"><a href="coh_sp.html#K22" title="COH_SP:func.22">cod</a> <font color="Maroon" title="c3">m2</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">m2</font> <a href="xfamily.html#K2" title="XFAMILY:func.2">`2</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">m1</font> <a href="xfamily.html#K2" title="XFAMILY:func.2">`2</a></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> = 
<font color="Maroon" title="c3">m2</font> <a href="coh_sp.html#K24" title="COH_SP:func.24">*</a> <font color="Maroon" title="c2">m1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="coh_sp.html#D24" target="_self" onmouseover="rs('coh_sp/D24')" onmouseout="rh()">Def23</a></span>
<br/>.= 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3">(<span class="default"><a href="coh_sp.html#K21" title="COH_SP:func.21">dom</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">m2</font> <a href="coh_sp.html#K24" title="COH_SP:func.24">*</a> <font color="Maroon" title="c2">m1</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="coh_sp.html#K22" title="COH_SP:func.22">cod</a> <span class="p4">(<span class="default"><font color="Maroon" title="c3">m2</font> <a href="coh_sp.html#K24" title="COH_SP:func.24">*</a> <font color="Maroon" title="c2">m1</font></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">m2</font> <a href="coh_sp.html#K24" title="COH_SP:func.24">*</a> <font color="Maroon" title="c2">m1</font></span>)</span> <a href="xfamily.html#K2" title="XFAMILY:func.2">`2</a></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="coh_sp.html#T42" target="_self" onmouseover="rs('coh_sp/T42')" onmouseout="rh()">Th41</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E3:76"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c3">m2</font> <a href="coh_sp.html#K24" title="COH_SP:func.24">*</a> <font color="Maroon" title="c2">m1</font></span>)</span> <a href="xfamily.html#K2" title="XFAMILY:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">m2</font> <a href="xfamily.html#K2" title="XFAMILY:func.2">`2</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m1</font> <a href="xfamily.html#K2" title="XFAMILY:func.2">`2</a></span>)</span> &amp;  <a href="coh_sp.html#K21" title="COH_SP:func.21">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">m2</font> <a href="coh_sp.html#K24" title="COH_SP:func.24">*</a> <font color="Maroon" title="c2">m1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K21" title="COH_SP:func.21">dom</a> <font color="Maroon" title="c2">m1</font> &amp;  <a href="coh_sp.html#K22" title="COH_SP:func.22">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">m2</font> <a href="coh_sp.html#K24" title="COH_SP:func.24">*</a> <font color="Maroon" title="c2">m1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="coh_sp.html#K22" title="COH_SP:func.22">cod</a> <font color="Maroon" title="c3">m2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="coh_sp.html#E31"><span class="lab"><font color="Green" title="E16">Lm2</font></span></a>, <a class="ref" href="xtuple_0.html#T1" onmouseover="rs('xtuple_0/T1')" onmouseout="rh()">XTUPLE_0:1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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