reason_title=mult_neg,\
	div_neg,\
	add_neg,\
	div_zero,\
	mult_zero,\
	mult_nochain,\
	add_sign,\
	trans_eq,\
	lose_eq,\
	square,\
	abs,\
	alg_err,\
	illegal,\
	bad_trans,\
	bad_chain

reason_name=multiply by negative number should inverse the inequality,\
	divide by negative number should inverse the inequality,\
	add a negative number does not inverse the inequality,\
	possibility of division by zero,\
	multiply by 0 does not preserve a strict inequality,\
	a&lt;b et c&lt;d do not imply ac&lt;bd,\
	sign error in addition of a term,\
	equality lost after transitivity,\
	the case of equality is lost without reason,\
	error in the manipulation of square,\
	error in the manipulationof absolute value,\
	error in algebraic operations,\
	illegal operation,\
	bad application of transitivity,\
	bad chaining of inequalities
	
reason_title2=mult_neg2,\
	div_neg2,\
	add_neg2,\
	trans_eq2,\
	add_eq2

reason_name2=multiplication should preserve the inequality,\
	division should preserve the inequality,\
	add a negative number should inverse the inequality,\
	equality added after transitivity,\
	equality case added without reason

no_name=this step is wrong

