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<span class="kw">let </span><font color="Maroon" title="c1">CL</font> be   <a href="lattices.html#NM7" title="LATTICES:NM.7">C_Lattice</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">IL</font> being  <a href="filter_0.html#V3" title="FILTER_0:attr.3">implicative</a>  <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a><br/> for <font color="Olive" title="b2">f</font> being   <a href="lattice4.html#M1" title="LATTICE4:mode.1">Homomorphism</a> of <font color="Olive" title="b1">IL</font>,<font color="Maroon" title="c1">CL</font>  st <font color="Olive" title="b2">f</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  holds <br/>( <font color="Maroon" title="c1">CL</font> is  <a href="filter_0.html#V3" title="FILTER_0:attr.3">implicative</a>  &amp; <font color="Olive" title="b2">f</font> <a href="lattice4.html#R1" title="LATTICE4:pred.1">preserves_implication</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">IL</font> be   <a href="filter_0.html#V3" title="FILTER_0:attr.3">implicative</a>  <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</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">f</font> being   <a href="lattice4.html#M1" title="LATTICE4:mode.1">Homomorphism</a> of <font color="Maroon" title="c2">IL</font>,<font color="Maroon" title="c1">CL</font>  st <font color="Olive" title="b1">f</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  holds <br/>( <font color="Maroon" title="c1">CL</font> is  <a href="filter_0.html#V3" title="FILTER_0:attr.3">implicative</a>  &amp; <font color="Olive" title="b1">f</font> <a href="lattice4.html#R1" title="LATTICE4:pred.1">preserves_implication</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">f</font> be    <a href="lattice4.html#M1" title="LATTICE4:mode.1">Homomorphism</a> of <font color="Maroon" title="c2">IL</font>,<font color="Maroon" title="c1">CL</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="c3">f</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  implies ( <font color="Maroon" title="c1">CL</font> is  <a href="filter_0.html#V3" title="FILTER_0:attr.3">implicative</a>  &amp; <font color="Maroon" title="c3">f</font> <a href="lattice4.html#R1" title="LATTICE4:pred.1">preserves_implication</a>  ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:41"/><span class="lab"><font color="Green" title="E29">A1</font></span>: 
<font color="Maroon" title="c3">f</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</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">CL</font> is  <a href="filter_0.html#V3" title="FILTER_0:attr.3">implicative</a>  &amp; <font color="Maroon" title="c3">f</font> <a href="lattice4.html#R1" title="LATTICE4:pred.1">preserves_implication</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E2:41"/>
<font color="Maroon" title="c1">CL</font> is  <a href="filter_0.html#V3" title="FILTER_0:attr.3">implicative</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="c3">f</font> <a href="lattice4.html#R1" title="LATTICE4:pred.1">preserves_implication</a> </span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">p</font>, <font color="Maroon" title="c5">q</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">CL</font>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="filter_0.html#D7" title="FILTER_0:def.7">FILTER_0:def 7</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">CL</font> st <br/>( <font color="Maroon" title="c4">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#R1" title="LATTICES:pred.1">[=</a> <font color="Maroon" title="c5">q</font> &amp; ( for <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">CL</font>  holds <br/>(  not <font color="Maroon" title="c4">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive">b<sub>2</sub></font> <a href="lattices.html#R1" title="LATTICES:pred.1">[=</a> <font color="Maroon" title="c5">q</font> or <font color="Olive">b<sub>2</sub></font> <a href="lattices.html#R1" title="LATTICES:pred.1">[=</a> <font color="Olive">b<sub>1</sub></font> ) ) )</span><br/>

<span class="kw">consider </span><font color="Maroon" title="c6">i</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">IL</font><span class="kw"> such that </span><br/><a NAME="E2:41_1"/><span class="lab"><font color="Green" title="E30">A2</font></span>: 
<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:41"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="ref" href="lattice4.html#T9" target="_self" title="LATTICE4:th.9">Th9</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c7">j</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">IL</font><span class="kw"> such that </span><br/><a NAME="E4:41_1"/><span class="lab"><font color="Green" title="E31">A3</font></span>: 
<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">q</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:41"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="ref" href="lattice4.html#T9" target="_self" title="LATTICE4:th.9">Th9</a></span>;<br/>
<span class="kw">take </span><font color="Maroon" title="c8">r</font> = <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">i</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c7">j</font></span>)</span>; <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="c4">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Maroon" title="c8">r</font> <a href="lattices.html#R1" title="LATTICES:pred.1">[=</a> <font color="Maroon" title="c5">q</font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">CL</font>  holds <br/>(  not <font color="Maroon" title="c4">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#R1" title="LATTICES:pred.1">[=</a> <font color="Maroon" title="c5">q</font> or <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#R1" title="LATTICES:pred.1">[=</a> <font color="Maroon" title="c8">r</font> ) ) )</span><br/>

<span class="kw">thus </span><a NAME="E5:41_1"/>
<font color="Maroon" title="c4">p</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c8">r</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c5">q</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:41_1"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="txt" href="#E4:41_1"><span class="lab"><font color="Green" title="E31">A3</font></span></a>, <a class="ref" href="lattice4.html#T33" target="_self" title="LATTICE4:th.33">Th33</a></span>; <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">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">CL</font>  holds <br/>(  not <font color="Maroon" title="c4">p</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#R1" title="LATTICES:pred.1">[=</a> <font color="Maroon" title="c5">q</font> or <font color="Olive">b<sub>1</sub></font> <a href="lattices.html#R1" title="LATTICES:pred.1">[=</a> <font color="Maroon" title="c8">r</font> )</span><br/>

<div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span>
<div class="add"><span class="kw">let </span><font color="Maroon" title="c9">r1</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">CL</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="c4">p</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c9">r1</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c5">q</font> implies <font color="Maroon" title="c9">r1</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c8">r</font> )</span><br/><span class="kw">assume </span><a NAME="E1:41_1_1"/><span class="lab"><font color="Green" title="E32">A4</font></span>: 
<font color="Maroon" title="c4">p</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c9">r1</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c5">q</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="c9">r1</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c8">r</font></span><br/><a NAME="E2:41_1_1"/>
 ex <font color="Olive" title="b1">k</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">IL</font> st <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">r1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:41"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="ref" href="lattice4.html#T9" target="_self" title="LATTICE4:th.9">Th9</a></span>;<br/><span class="kw">hence </span><a NAME="E3:41_1_1"/>
<font color="Maroon" title="c9">r1</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c8">r</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:41"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="txt" href="#E2:41_1"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="txt" href="#E4:41_1"><span class="lab"><font color="Green" title="E31">A3</font></span></a>, <a class="txt" href="#E1:41_1_1"><span class="lab"><font color="Green" title="E32">A4</font></span></a>, <a class="ref" href="lattice4.html#T34" target="_self" title="LATTICE4:th.34">Th34</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>


</div><span class="kw">end;</span></div>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">CL</font> = <font color="Maroon" title="c1">CL</font> as   <a href="filter_0.html#V3" title="FILTER_0:attr.3">implicative</a>  <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">f</font> = <font color="Maroon" title="c3">f</font> as    <a href="lattice4.html#M1" title="LATTICE4:mode.1">Homomorphism</a> of <font color="Maroon" title="c2">IL</font>,<font color="Maroon" title="c4">CL</font> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">i</font>, <font color="Maroon" title="c7">j</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">IL</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">i</font></span>)</span> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">j</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">i</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c7">j</font></span>)</span></span><br/><div><span class="lab"><font color="Green" title="E30">A5</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="41_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c8">r1</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">CL</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">i</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c8">r1</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">j</font> implies <font color="Maroon" title="c8">r1</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">i</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c7">j</font></span>)</span> )</span><br/><span class="kw">assume </span><a NAME="E1:41_2_1"/><span class="lab"><font color="Green" title="E31">A6</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">i</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c8">r1</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">j</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="c8">r1</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">i</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c7">j</font></span>)</span></span><br/><a NAME="E2:41_2_1"/>
 ex <font color="Olive" title="b1">k</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">IL</font> st <font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">r1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:41"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="ref" href="lattice4.html#T9" target="_self" title="LATTICE4:th.9">Th9</a></span>;<br/><span class="kw">hence </span><a NAME="E3:41_2_1"/>
<font color="Maroon" title="c8">r1</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">i</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c7">j</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:41"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="txt" href="#E1:41_2_1"><span class="lab"><font color="Green" title="E31">A6</font></span></a>, <a class="ref" href="lattice4.html#T34" target="_self" title="LATTICE4:th.34">Th34</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E2:41_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">i</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">i</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c7">j</font></span>)</span></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">j</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="lattice4.html#T33" target="_self" title="LATTICE4:th.33">Th33</a></span>;<br/><span class="kw">hence </span><a NAME="E3:41_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">i</font></span>)</span> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">j</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">i</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c7">j</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:41_2"><span class="lab"><font color="Green" title="E30">A5</font></span></a>, <a class="ref" href="filter_0.html#D8" title="FILTER_0:def.8">FILTER_0:def 8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E6:41"/>
<font color="Maroon" title="c3">f</font> <a href="lattice4.html#R1" title="LATTICE4:pred.1">preserves_implication</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="lattice4.html#D6" target="_self" title="LATTICE4:def.6">Def6</a></span>; <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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