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<b>reconsider </b><font color="Maroon" title="c1">IT</font> =  <a href="bcialg_4.html#K2" title="BCIALG_4:func.2">BCI_S-EXAMPLE</a>  as   <a href="bcialg_4.html#NM2" title="BCIALG_4:NM.2">BCK-Algebra_with_Condition(S)</a> ;<br/>
<a NAME="E2:70_1_1"/>
<font color="Maroon" title="c1">IT</font> is <a href="bcialg_4.html#V4" title="BCIALG_4:attr.4">positive-implicative</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="70_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">IT</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="bcialg_4.html#D11" target="_self" title="BCIALG_4:def.11">BCIALG_4:def 11</a><br/>

<b>thus </b><a NAME="E1:70_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Maroon" title="c3">y</font>
 <b>by </b><i><a class="ref" href="struct_0.html#D10" title="STRUCT_0:def.10">STRUCT_0:def 10</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:70_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being  <a href="bcialg_4.html#NM2" title="BCIALG_4:NM.2">BCK-Algebra_with_Condition(S)</a> st <font color="Olive">b<sub>1</sub></font> is <a href="bcialg_4.html#V4" title="BCIALG_4:attr.4">positive-implicative</a>
 ;<br/>


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