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MatPlus.Net Forum General A question aboute ’consequent helpmate’ (hc#)
 
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(21) Posted by Michel Caillaud [Monday, Dec 20, 2010 20:48]

Very good improvement of Jean-Christian's idea, Valery! without promoted force on the board!
Re-reading what I wrote at the time, I discover that I was against applying the term consequent to helpmate. I didn't remember that (amnesia?) and today cannot understand exactly why...
The main difference that can be seen between consequent and amnesia, limiting to orthodox rules, seems to concern en passant. For castling, the implications look to be the same...
 
   
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(22) Posted by Bojan Basic [Tuesday, Dec 21, 2010 03:49]; edited by Bojan Basic [10-12-21]

I would state the main difference between consequtive and Amnésie as follows:
• in consequent series-movers, all the intermediary positions during the series of consequtive moves of the same side are evaluated independently of each other;
• with Amnésie, all the positions (even when the other side gets on the move) are evaluated independently of each other.

 QUOTE 
For castling, the implications look to be the same...

Actually, I think that the castling rights can also depend on whether we are considering ’consequent’ or ’Amnésie’. Look at the following scheme:

(= 4+8 )

a) ser-hc#2;
b) Amnésie, ser-h#2.

Solution 1.c7-c6 2.Bf1*g2 0-0-0 # works for b), but not for a). Indeed, if the last move Black’s move is known to be Bf1*g2 (what is known in a), but not known in b)), then Black had to promote on f1 earlier in the game, what destroyed White’s castling rights.

And I use this opportunity to name a few of many examples in the fairy realm where possible moves of one side depend on the previous play, and thus the mentioned difference can be manifested: fairy pieces Joker, Invisibles, Variables... and fairy conditions Frischauf Circé, Volages, Follow-my-leader (or Pursuit chess), Duel chess, One-way chess, Disguised Kings, All-in chess, Patience chess, Disparate, Camouflage Kings, Turbo chess...
 
   
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(23) Posted by Valery Liskovets [Tuesday, Dec 21, 2010 14:32]

Michel, perhaps you made difference between consequent and amnesia as terms because of your recurrent definition of the former? Or merely because of revealing the intention of your fine amnesic ser-h#8 problem 2002 (which I mentioned formely)?

I initially underestimated the influence of this concept on e.p. but presently don't see serious dangerous.

For me, "consequent" (a somewhat enigmatic term, indeed, but relevant nonetheless, IMHO) means just what it does in ordinary helpmates! I.e. equivalent to (homogeneous) amnesia. In series helpmates, instead, we have one exceptional non-serial concluding move of the opposite side. It is exceptional not only w.r.t. amnesia. Almost any extra restriction should have a special indication as to this move. So, for series helpmates we have, indeed, 2 sub-genres: ordinary consequent and amnesia. Mishel's problem and both Bojan's examples show well their subtle distinction. But when this last move has nothing to do with e.p. and castling, the distinction disappears; and it does not arise at all for non-series helpmates. Ok?

I do not object against the term "amnesia". I only reject the use of absolutely distinct terms for very similar conditions. Even in your, Bojan, quite general definition (much more general than series-helpmates need!) I'd prefer to utilize related terms; say, 1-sided and 2-sided amnesias (or black and black-and-white amnesias, resp.). Perhaps your definition makes sense for additional fairy conditions. But this goes far from my knowledge. Usually such unifications require long discussions between experts. Most urgent, in my opinion, is to analyze the application of these amnesic ideas to parry series... But anyway I prefer to consider these as SUB-GENRES of a general genre that has a certain (generic) name. No matter, will it be "amnesia" or "consequent" (or even both as synonyms co-existing by historical reasons!).
 
 
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(24) Posted by Kevin Begley [Tuesday, Dec 21, 2010 15:13]; edited by Kevin Begley [10-12-21]

There is another mildly interesting point to be made here...

There is a difference between common form, series-consequent-helpmate (serc-h#n), and the unused alternative, series-help-consequent-mate (ser-hc#n).

It easiest to describe this difference via an alternative formal stipulation mechanism, based upon sub-goals (which must be solved iteratively, unto finality).
However, presently this would require significant explanation (and a major overhaul of currently inconsistent classifications).
So, instead, I'll simply describe the process involved...

In the former (commonly used) form -- serc-h#n:
Black plays n-1 moves under a combination of "series" and "consequent" fairy conditions, intending to reach the sub-goal (achieve a position with hc#1).
By iteration, the sub-goal -- hc#1 -- is then evaluated:
Black plays 1 move, under the same combination of fairy conditions, intending to reach the next sub-goal (achieve an orthodox #1).
Note: up to this point, black may have castled a few dozen times...
After one last iteration (White plays 1 orthodox move) we reach finality -- the aim of the problem: black stands checkmated (#).

In the latter (thus far unused) form -- ser-hc#n:
Black plays n-1 moves under only the "series" condition, intending to reach the sub-goal (achieve a position with hc#1).
Again, by iteration, the sub-goal -- hc#1 -- is then evaluated:
Black plays 1 move, under "series" and "consequent" fairy conditions, intending to reach the next sub-goal (achieve an orthodox #1).
Note: only on this one move does the consequent condition apply.
After one last iteration, again, we reach the final aim.

There are two points to be made here on the advantages of a goals-based mechanism:
1) A logical, clear and consistent methodology is possible, to formally stipulate a solver's task (minimizing doubt/space), and
2) This methodology would open up rich possibilities.

It may seem that the later form offered (ser.hc#n) has few prospects (the consequent condition is barely employed, after all).
However, this estimation is rooted in the frequent, flawed assumption that all sub-goals must be a single move deep.
Think outside of the box...

Michel Caillaud
Help-Direct-Mate TT, 2005
(= 3+6 )

Win Chloe stipulates this as: "h4#2", (essentially, an extension of the "blunder-mate" idea).

solution: 1.d1=S! g5 2.e1=R! g6 3.Rg1 g7 4.f1=B! & 1.g8=Q! [> 2.Qg3#]

From an iterative sub-goal perspective, each sub-goal iteration should appear in parenthesis -- e.g., something like: h4(#2).
This opens up many diverse opportunities, without having to resort to countless new names.
[note: I'll not get into the specifics of the mechanism I would suggest to stipulate this task, as might cause confusion w/o proper context.]

Furthermore, each sound problem becomes a "virtual machine" -- one need only wrap parenthesis around the task, and move up one level.

Finally, consider how such a methodology removes the separation between Amnesia versus Consequent.
They become unified into a singular (and fundamental) fairy condition -- it is only a matter of which sub-goals apply this condition!
[As I understand it, only the final sub-goal differs: in Consequent the final goal is "#1", whereas in Amnesia it is "consequent-#1"]
And, newcomers need not be concerned -- ever again! -- about the trivial specifics of the countless extraneous names given unto tasks.

[ps: it is also worth noting some terms (e.g., 'semi-reflex') disappear -- often, they can be completely described at a more fundamental level (w/o any conditions).]
 
   
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(25) Posted by Hauke Reddmann [Wednesday, Dec 22, 2010 14:12]

quote Kevin:
"Furthermore, each sound problem becomes a 'virtual machine' -- one need only wrap parenthesis around the task, and move up one level."

Chess as a Turing machine (infinite board or internal states required)?
Why not? Minesweeper ist Turing-equivalent either :-)

Hauke
 
   
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(26) Posted by Michel Caillaud [Thursday, Dec 23, 2010 15:43]; edited by Michel Caillaud [10-12-23]

Most intervenants (Valery, Bojan, Kevin, I...) agree that an unifying approach is desirable.
Kevin's approach is still more general but concentrating on consequent would be a first step...
Starting from Bojan's formulations, one can fuse the two of them in one :

Every position is evaluated independently after every move of the solution.

This cover serie-problems and problems with alternance of white and black moves (helpmates, directmates, selfmates,...).
This seems to be applicable definition for both consequent helpmate by Valery and Amnesia from France-Echecs.
Perhaps, the term consequent would be the desirable (?) unifying term.

In serie-problems, the situation is complicated by additional question of the "sub-goal" that has to be precised as underlined by Bojan's example and Kevin's arguments.
There can be serc-h# (Bojan's a), ser-hc# (Bojan's b) or serc-hc#!
"Historical" shc# is serc-h#

Also Kevin's final "orthodox 1#" has to be questioned.
A consequent 1# is when (White) plays and obtains a position where (Black) is mate.

Here is an illustration :

(= 4+5 )

a) h#2 b) hc#2 (4+5)

a) 1.Ka4 Lxc6+ 2.b5 cxb6 e.p.#
this solution doesn't work in b) : the position after 2.b5, evaluated independantly, is not an "orthodox 1#"
b) 1.a4 Ld3+ 2.Ka5 b4#
the position after 2...b4, evaluated independantly, is a mate position.

As stated before, the general principle can be applied to direct problems.
Here is an illustration implying the 2 main tricks (in orthodox play) :

(= 6+5 )

c#2 (7+5)

1.0-0#? is illegal as black King had to reach a1 via d2 or d1.
After playing Pawn c2, 0-0 "becomes" legal.
1.c3? dxc3!
1.c4! ~ 2.0-0#
 
   
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(27) Posted by Kevin Begley [Thursday, Dec 23, 2010 20:15]; edited by Kevin Begley [10-12-24]

Well said (and illustrated), Michel.

>There can be serc-h# (Bojan's a), ser-hc# (Bojan's b) or serc-hc#! ("Historical" shc# is serc-h#)

There might be two types of help-consequent-mates, as well: hc2(c#1), and hc2(#1).
In the second phase -- b) hc#2 -- of your first example, you must be referring to hc2(c#1); otherwise, it is not mate (3.axb3ep!).
However, the first phase -- a) h#2 -- could equally be written as hc2(#1) -- the solutions should be equivalent.
Agreed?

Is it possible to show all three possibilities -- a) h2(#1), b) hc2(#1), and c) hc2(c#1) -- in three distinct phases of a single, orthodox problem?
Would additional moves, or an additional fairy element, be required?

What about adding the fourth (and final) possibility: d) h2(c#1)?

[edit: I'm wrong, there are 7 (seven!) distinct forms of consequent helpmates... see my post below.]
 
   
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(28) Posted by Valery Liskovets [Thursday, Dec 23, 2010 22:13]

For me, Michel, your general suggestion looks convincing and attractive. Hopefully it is consistent. As to your twins a) h#2 b) hc#2, they are better than my similar problem which is to be (or was?) published in Die Schwalbe. There is a different example:

VL, The Problemist, Sep 2010
(= 6+5 )

a) h#2 b) hc#2

a) 1.Rhe8 Bh4+ 2.g5 hxg6 e.p.#; b) 1.Ke8 Bg3 2.0-0-0 Sb6#.
 
   
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(29) Posted by Kevin Begley [Thursday, Dec 23, 2010 23:03]; edited by Kevin Begley [10-12-24]

>A consequent 1# is when (White) plays and obtains a position where (Black) is [checkmated]

It seems to me there are even alternative types of 'consequent-#1', though perhaps the semantics remain a source of confusion...
The issue here is that the consequent condition may apply after the mate is played.

To clarify this, let's turn the stipulation inside out -- numbers first, then move types, sub-goals in parenthesis, and the aim in brackets.
So, h#2 would read: "2h(1[#])" -- aim [#], goal (1#), play "2h()".

scheme
(= 6+3 )

help-consequent-#1
Circe + white must give priority to captures

a) 1h(1[#]) ? <= equivalent to h#1
b) 1h(1c[#]) ?
c) 1h(1[c#]) ?
d) 1h(1c[c#]) ?

[edit: In none of the above does the consequent condition apply to black's moves -- if it did, 4 additional possibilities would emerge.]

a) has no solution.

1.a7-a5 must be answered by 1...bxa6ep (priority to captures); and, even if white could play 1...b2-b4+, black would defend with:
2.axb3ep[+wPb2]!

b) has no solution.

Now, 1.a7-a5 can be answered by 1...b2-b4+, but this does not meet the aim ['orthodox mate'], because black may respond with 2.axb3ep [+wPb2]!

c) has no solution.

1.a7-a5? does not work, because white's play is not consequent (only the final aim is), thus white must respond 1...bxa6ep (giving priority to captures).

d) (only) has a solution.

Now, after 1.a7-a5, white can forget about the previous move (which can not be proven), and respond with 1...b2-b4 c#!

This single fairy condition may be independently applied within the aim, the goal, or the outer layers of the play (here there is 1 outer layer, but there may be more).

Thus, when you say 'consequent-1#,' I see 3 possible meanings: 1c[#], 1[c#], and 1c[c#]
(where c = the single, unifying fairy condition, which governs the legality of moves -- I'll leave it to the experts to decide what its name should be.)

My present understanding is that h#1 + amnesia would currently be translated into: 1hc(1c[c#]).
This is logical, fairy conditions generally apply at all levels (aim, goal, play).
I believ Valery's hc#1 would be translated into: 1hc(1[#]) -- if I understand it correctly.
Please correct me if I have these wrong.
 
   
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(30) Posted by Michel Caillaud [Friday, Dec 24, 2010 15:05]

hum... I see that my "unifying" definition is more or less the same than the one of Amnesia given by Bojan in the initial post of this discussion; we live in a small world...

@Valery
Oops, sorry; I didn't yet receive the December issue of Die Schwalbe; I was still thinking you were working only on castling, as indicated in your article in StrateGems. Now I see you have since integrated en passant in your hc#s with your Problemist problem and also your 14572 in Die Schwalbe 244 (August)

@Kevin
I think I see your point.
Your example is confusing as there is always the move a5xb4(b2).
Well, I think there are the theoritical possibilities and the interesting ones among them (and this last point is of course subjective). I see no point to refuse 2...c5xb6 e.p. and accept 3.a4xb3 e.p. in the same problem, though I admit this can "theoritically" be elaborated.
As a solver, if I see a lot of () and [] in a stipulation, I think I will flee...
I am in favour of compact presentation for "homogeneous" content :
h# : everything is orthodox
hc# : everything is consequent, mate included.
The "inhomogeneous" content, theoritically possible, would require more elaborated presentation as you suggest.
The serie problem is sligthly more complicated as there are two parts, separated by the change of alternance of the moves (non alternance in the first part, alternance in the final part). Again, I am mostly interested in the case where each part is "homogeneous".

But... my family say : "enough of that".
So:
Merry Christmas!!
 
   
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(31) Posted by Kevin Begley [Saturday, Dec 25, 2010 01:49]; edited by Kevin Begley [10-12-25]

Sorry for the lousy scheme I provided... indeed, it does depend on a7 (an afterthought) having no rights to capture.

>"As a solver, if I see a lot of () and [] in a stipulation, I think I will flee..."

I do agree there... in most cases, the brackets and parenthesis disappear (e.g., if consistency may be assumed, and the goal is 1 ply).
The exceptions are rarely employed -- and should probably be used only to good purpose.

My interest is slightly more academic -- to establish a consistent notation fully describing formalized chess problem tasks.
And, clarification does remain a work in progress... I am hopeful that something easier (than our current system) will soon emerge.
Happy Holidays.
 
   
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(32) Posted by Joost de Heer [Saturday, Dec 25, 2010 10:26]

 QUOTE 

My interest is slightly more academic -- to establish a consistent notation fully describing formalized chess problem tasks.

Have you looked at the sstip implementation of Popeye?
 
 
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(33) Posted by Valery Liskovets [Saturday, Dec 25, 2010 15:24]; edited by Valery Liskovets [10-12-30]

Michel wrote:
>"I was still thinking you were working only on castling, as indicated in your article in >StrateGems. Now I see you have since integrated en passant in your hc#s"

Yes. As I wrote in the article, "such a fairy variation makes sense mainly with
respect to castling". The very first consequent helpmate with e.p. is my retro-problem published in StrateGems in July (PDB's P1109965). It was composed after I'd submitted my article but could be published simultaneously with (or even inside) it. However I preferred not to fuss. (See also http://www.pairlist.net/pipermail/retros/2010-April/003232.html .)

I share Michel's doubts wrt too sophisticated stipulations/restrictions/aims.
 
   
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(34) Posted by Kevin Begley [Saturday, Dec 25, 2010 17:14]; edited by Kevin Begley [10-12-25]

@Joost,

Yes, but only enough to realize that sstip does not -- and, is not designed to -- solve the consistency and non-redundancy problem.
This can only be achieved by consistently defining the elements of a task (start from aims, build your way up to fairy conditions).
After some time spent considering the problem, an iterative sub-goals based process still seems, to me, the optimal descriptive solution.

There may be alternative solutions, but I do not see that sstip offers one.

And, for the record...
Many might flee a problem in which the fairy piece was described as: (2,3:0,2)DecomposedLeaperRiderContraHopper.
Nevertheless, I consider this description to serve a vital function: it offers us a consistent, non-redundant classification of fairy pieces.
...and, it leaves no need for mnemonics.
 
   
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(35) Posted by Michel Caillaud [Tuesday, Jan 4, 2011 07:20]

Happy New Year 2011 to everybody!!

@Valery
Die Schwalbe arrived last day of last year.
What I like in your rendering is that major pieces have active role in both solutions. In mine, black figures have only anti-cook function.
 
   
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(36) Posted by Valery Liskovets [Tuesday, Jan 4, 2011 12:08]

@Michel,

Thanks for informing me about the publication in die Schwalbe (I'm not a subscriber)! Anyway, your light implementation is excellent and MUCH better than mine. Both are the only non-retro consequent helpmates without castling.
 
   
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(37) Posted by Sarah Hornecker [Wednesday, Jan 5, 2011 01:04]

When I was still younger than I am now, proof issues of Die Schwalbe were still sent to composers. I don't think this has changed. So if you don't receive a proof issue in due time, make sure to complain at the editor. :-)
 
   
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(38) Posted by Kevin Begley [Wednesday, Jan 5, 2011 11:08]; edited by Kevin Begley [11-01-05]

One question still troubles me about the consequent/amnesia condition...
Suppose, in the course of a solution, I arrive at a co-dependent position -- for example:

Scheme (based entirely upon W.Langstaff's famous #2):
(= 4+3 )

hc#1.5 A.P. ??

Here we find simple co-dependence:
If black can castle, en passant must be legal; otherwise, en passant can not be proven, and must be assumed to be illegal.

The "A Posteriori" (A.P.) condition allows the solver to take action (e.g., capture by en passant), providing proof is later furnished (by actually castling!) that the assumed legality of castling was, in fact, correct.

So, suppose white plays 1...exd6ep! (arguing that proof will be furnished later)...
Except, when it comes time to prove castling legal, a selective form of conditional amnesia sets in...
After all, this position does constitute an entirely new diagram (with no strings attached)!
So, rather than castling (to establish, after the fact, the legality of the en passant capture), the solver continues with:
2.Tf8! ...d7#.

I realize it is easy to wave-off this matter -- when two (or more) fairy elements are employed, the burden rests upon the composer to account for the possibility of any ambiguous interaction.
But, my scheme is only intended to demonstrate the mechanism of selective amnesia.

The real issue here is when co-dependence is applied to retro-variants -- which were, fairly recently, adopted by the Codex (read: these are not a secondary fairy element!).

Consider the retro-variants of W.Langstaff's problem, if the stipulation is changed to: consequent-#2.
By Codex, the White-side must separate the problem into two cases, and prove both allow #2.

So, suppose White first considers the case where castling and en passant are both legal...
After white plays the standard en passant capture, black has no defense against mate.

But, in the second case, where en passant can not be played, can the black-side employ a strategy of "selective amnesia," to defend against the mate (by castling anyway!)?
Consequent rules would seem to allow this.

And, if white expects this defense-by-amnesia, can it be countered by employing an offensive strategy of selective amnesia (read: oops, I forgot entirely about the need to establish the alternative case).

I wish I had time (at the moment) to compose a clear example of this dilemma...
But, I don't want to wait to learn whether a contingency is already established for this bizarre possibility...

If this has already been covered, could somebody please furnish the full definitions of the consequent/amnesia conditions?

If not, I would humbly suggest postponing any redefinition...
It would seem wise to first encourage persuasive-compositions, which cleverly exaggerate this ambiguity (for entertainment).
 
   
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(39) Posted by Valery Liskovets [Wednesday, Jan 5, 2011 12:36]; edited by Valery Liskovets [11-01-05]

@Kevin,

I don't catch all details of your reasonings but can comment some.

1. The AP logic is strongly opposed to that of PRA by Langstaff, Loyd, Dawson, Ceriani et al. Therefore for AP, it's unnatural to refer to Langstaff. Instead, the pioneer AP-problem P0003417 by J.F.Keeble, 1936 (the 75-year jubilee, btw!), is more suitable. Your scheme resembles it.

2. Regardless of the current status of the Codex, AP is not a fairy genre. Controversial (and presently conditional), yes...

3. Controversial genres (ways to interpret and use co-dependences) including PRA, AP and RS (retro-strategy) are based upon a very good memory, contrarily to consequent/amnesia! Therefore at least presently I don't see a natural way to combine both concepts (well, let amnesia be selective but how can it be natural in a sense and leave simultaneously enough co-dependences?).
 
   
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(40) Posted by Kevin Begley [Thursday, Jan 6, 2011 01:00]

Valery,

>3. Controversial genres (ways to interpret and use co-dependences) including PRA, AP and RS (retro-strategy) are based upon a very good memory, contrarily to consequent/amnesia!

This term may hold for AP, and RS... but, how can you possibly call PRA (which is now accepted by the Codex -- see Chapter 4, Article 16:3) controversial?

>...Therefore at least presently I don't see a natural way to combine both concepts (well, let amnesia be selective but how can it be natural in a sense and leave simultaneously enough co-dependences?).

But, that's my point... PRA and Consequent/Amnesia must be combined, somehow, for completeness.
The condition could attempt to forbid (by definition) the use of PRA... but, such an act could lead to a "grey goo" scenario.
If you render illegal PRA, by the condition's definition, does it become illegal to wander into such a co-dependent position?

Such a thing can lead to remarkably unexpected results!
In the fairy condition Rex Multiplex, for example, it is illegal to mate a single royal-unit.
At first, this definition may seem simple enough... but, then you discover how a single-royal-mate avoidance can cause retro-feedback catastrophe (the implications of a few moves before you, can fast overwhelm the legal assessment of positions many plies behind you).

There is a phenomenon which I call, "Fairy-Radiation" -- the more complex a fairy condition, the more unstable it becomes.
If a condition allows a legal-feedback loop (e.g., once co-dependent positions become illegal, any position which leads only to co-dependence must become illegal too!), inherently, the condition risks exceeding critical mass.

Thus, when confronted with the possibility of a co-dependent position, consequent/amnesia must provide some method to resolve the legalities, under PRA (in accordance with the Codex).

We can agree that AP and RS "genres" (these are retro-conditions in my eyes) need not be treated -- the inventor of a fairy condition (consequent/amnesia) need not reconcile its behavior when mixed with additional fairy elements.

But, all legal cases must be reconciled -- that means, under chapter 4 of the Codex (article 16:3), PRA must be treated.
 
   
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MatPlus.Net Forum General A question aboute ’consequent helpmate’ (hc#)