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!set methtit=Add two inequalities

!set methenv=ZZ QQ RR

!set methparmtype=parm inequality >,parm inequality >

!set methhelp=This method applies the following property on two existing\

inequalities, to deduce a third one:\

 <div class="wimscenter">\

 If \(a > b) and \(c > b), then \(a+c > b+d) .\

</div>\

 The last inequality will be put into the hypotheses.

!if $wims_read_parm iswordof form check

  !goto $wims_read_parm

!endif

!exit

:form

 Add the inequalities

!read deduc/methparm.phtml 1

 and

!read deduc/methparm.phtml 2

!exit

:check

!distribute items $methparmobj1 into data,left1,sign1,right1

!distribute items $methparmobj2 into data,left2,sign2,right2

methexp=Add \($left1 $sign1 $right1) and \($left2 $sign2 $right2)

gt=>

lt=<

!if ($gt isin $sign1 and $lt isin $sign2) or\

	($lt isin $sign1 and $gt isin $sign2)

  !exchange left2,right2

!endif

!read deduc/sub/simplify $left1 + ($left2)\

	$right1 + ($right2)

!distribute lines $out into newleft, newright

!if $newleft=$empty or $newright=$empty

  error=bad_data

  !exit

!endif

!if $gt isin $sign1

  s_=>

!else

  s_=<

!endif

eq=$empty=

!if $eq isin $sign1 and $eq isin $sign2

 s_=$s_=

!endif

newobject0=$newleft $s_ $newright

oldobject=0

contextlist=$ct_Always,\

	$ct_Onlywhen the two inequalities are positive,\

	$ct_Onlywhen one of the two inequalities is positive,\

	$ct_Onlywhen one of the two inequalities is of the same sign

!exit