The New Sudoku Players' Forum

[DEFISE]

I don't know what “assume A true => contradiction” means. In what context does this appear?

You have proved the confluence property in the case where we start from a valid RS and apply the BT (singles, box/line, subsets).
(i.e. final RS is independent of the order in which the BT are applied.)

But I don't think confluence property is true when you start from an invalid RS, for example when we assume a false candidate to be true and then we apply the BT and later you obtain a contradiction.
To check…

[denis_berthier]

Hi Denis,
It is good to have recognised an error in your demonstration invalidating Theorem 2-1,

You mean recognised it as soon as I found it, contrary to you, who waited 2 or 3 years before admitting an error in yours?
And you still have to admit that your proof of theorem 2.1 is false.

but it is even better to recognise that without my instance of saying that there was an anomaly you would not have noticed and would have persisted in invalidating this theorem.

After seeing you cheating with the "iff" or claiming you don't know what 2D-cells (what you have re-baptised "entities") are, I stopped reading your stuff.

I am satisfied that you conclude that Theorem 2-1 is valid,

Let it be clear: the theorem is valid for the full power of FOL (my first interpretation of your TR), but not for any TB, as you must have noticed from the previous posts. This makes it true for FOL but totally useless for your "theory".

I'm not interested in wasting more time with tracks.

[denis_berthier]

I don't know what “assume A true => contradiction” means. In what context does this appear?

You have proved the confluence property in the case where we start from a valid RS and apply the BT (singles, box/line, subsets).
(i.e. final RS is independent of the order in which the BT are applied.)
But I don't think confluence property is true when you start from an invalid RS, for example when we assume a false candidate to be true and then we apply the BT and later you obtain a contradiction.

The confluence property applies to a set of resolution rules. There's no starting from this or that.
Adding a candidate (true or false) merely amounts to starting from a different puzzle.