Using ordinary set theory, we can prove:

(1) ALL(a):[a in X & a=a] is FALSE for any set X.

Whereas

(2) ALL(a):[a in X => a=a]] is TRUE for any set X.

----------------------------------------------------------------------
PROOF (1)

Lemma: From Russel's Paradox (Proof: http://dcproof.com/UniversalSet.htm )

1. ALL(a):[Set(a) => EXIST(b):~b in a]
Axiom

Let x be a set

2. Set(x)
Premise

Apply lemma

3. Set(x) => EXIST(b):~b in x
U Spec, 1

4. EXIST(b):~b in x
Detach, 3, 2

5. ~y in x
E Spec, 4

6. ~y in x | ~y=y
Arb Or, 5

7. ~[~~y in x & ~~y=y]
DeMorgan, 6

8. ~[y in x & ~~y=y]
Rem DNeg, 7

9. ~[y in x & y=y]
Rem DNeg, 8

10. ALL(x):[Set(x) => EXIST(a):~[a in x & a=a]]
Conclusion, 2

11. ALL(x):[Set(x) => ~ALL(a):~~[a in x & a=a]]
Quant, 10

12. ALL(x):[Set(x) => ~ALL(a):[a in x & a=a]]
Rem DNeg, 11

----------------------------------------------------------------------
PROOF (2)

1. Set(x)
Premise

2. y in x
Premise

3. y=y
Reflex

4. ALL(a):[a in x => a=a]
Conclusion, 2

5. ALL(x):[Set(x) => ALL(a):[a in x => a=a]]
Conclusion, 1

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com

I guess its rather the paradox of irrelevance.
There are so many theorens that are irrelevant,
und would never make it into a paper, since

they use either inconsistent assumptions,
or then are non-construction and can therefore not be
applied. Are just some Unicorn dreams.

Maybe post some math when have outgrown your
juvenile phase of 1000-th version of Russels paradox
which is totally irrelevant and useless to mathematics.

Dan Christensen schrieb am Samstag, 3. Juni 2023 um 19:36:20 UTC+2:
> Using ordinary set theory, we can prove:
>
> (1) ALL(a):[a in X & a=a] is FALSE for any set X.
>
> Whereas
>
> (2) ALL(a):[a in X => a=a]] is TRUE for any set X.
>
> ----------------------------------------------------------------------
> PROOF (1)
>
> Lemma: From Russel's Paradox (Proof: http://dcproof.com/UniversalSet.htm )
>
> 1. ALL(a):[Set(a) => EXIST(b):~b in a]
> Axiom
>
> Let x be a set
>
> 2. Set(x)
> Premise
>
> Apply lemma
>
> 3. Set(x) => EXIST(b):~b in x
> U Spec, 1
>
> 4. EXIST(b):~b in x
> Detach, 3, 2
>
> 5. ~y in x
> E Spec, 4
>
> 6. ~y in x | ~y=y
> Arb Or, 5
>
> 7. ~[~~y in x & ~~y=y]
> DeMorgan, 6
>
> 8. ~[y in x & ~~y=y]
> Rem DNeg, 7
>
> 9. ~[y in x & y=y]
> Rem DNeg, 8
>
> 10. ALL(x):[Set(x) => EXIST(a):~[a in x & a=a]]
> Conclusion, 2
>
> 11. ALL(x):[Set(x) => ~ALL(a):~~[a in x & a=a]]
> Quant, 10
>
> 12. ALL(x):[Set(x) => ~ALL(a):[a in x & a=a]]
> Rem DNeg, 11
>
> ----------------------------------------------------------------------
> PROOF (2)
>
> 1. Set(x)
> Premise
>
> 2. y in x
> Premise
>
> 3. y=y
> Reflex
>
> 4. ALL(a):[a in x => a=a]
> Conclusion, 2
>
> 5. ALL(x):[Set(x) => ALL(a):[a in x => a=a]]
> Conclusion, 1
>
> Dan
>
> Download my DC Proof 2.0 freeware at http://www.dcproof.com
> Visit my Math Blog at http://www.dcproof.wordpress.com

Also for a moron like you it might not be evident
that you can replace a=a by TRUE. So you proved
these two theorems:

~ALL(a):[a e X]
TRUE

The first theorem has not even a mosquito leg
difference from your Universal Set theorem, at
least not in classical logic. And the second theorem,

is not something anybody would surprise.

Mild Shock schrieb am Samstag, 3. Juni 2023 um 20:10:13 UTC+2:
> I guess its rather the paradox of irrelevance.
> There are so many theorens that are irrelevant,
> und would never make it into a paper, since
>
> they use either inconsistent assumptions,
> or then are non-construction and can therefore not be
> applied. Are just some Unicorn dreams.
>
> Maybe post some math when have outgrown your
> juvenile phase of 1000-th version of Russels paradox
> which is totally irrelevant and useless to mathematics.
> Dan Christensen schrieb am Samstag, 3. Juni 2023 um 19:36:20 UTC+2:
> > Using ordinary set theory, we can prove:
> >
> > (1) ALL(a):[a in X & a=a] is FALSE for any set X.
> >
> > Whereas
> >
> > (2) ALL(a):[a in X => a=a]] is TRUE for any set X.
> >
> > ----------------------------------------------------------------------
> > PROOF (1)
> >
> > Lemma: From Russel's Paradox (Proof: http://dcproof.com/UniversalSet.htm )
> >
> > 1. ALL(a):[Set(a) => EXIST(b):~b in a]
> > Axiom
> >
> > Let x be a set
> >
> > 2. Set(x)
> > Premise
> >
> > Apply lemma
> >
> > 3. Set(x) => EXIST(b):~b in x
> > U Spec, 1
> >
> > 4. EXIST(b):~b in x
> > Detach, 3, 2
> >
> > 5. ~y in x
> > E Spec, 4
> >
> > 6. ~y in x | ~y=y
> > Arb Or, 5
> >
> > 7. ~[~~y in x & ~~y=y]
> > DeMorgan, 6
> >
> > 8. ~[y in x & ~~y=y]
> > Rem DNeg, 7
> >
> > 9. ~[y in x & y=y]
> > Rem DNeg, 8
> >
> > 10. ALL(x):[Set(x) => EXIST(a):~[a in x & a=a]]
> > Conclusion, 2
> >
> > 11. ALL(x):[Set(x) => ~ALL(a):~~[a in x & a=a]]
> > Quant, 10
> >
> > 12. ALL(x):[Set(x) => ~ALL(a):[a in x & a=a]]
> > Rem DNeg, 11
> >
> > ----------------------------------------------------------------------
> > PROOF (2)
> >
> > 1. Set(x)
> > Premise
> >
> > 2. y in x
> > Premise
> >
> > 3. y=y
> > Reflex
> >
> > 4. ALL(a):[a in x => a=a]
> > Conclusion, 2
> >
> > 5. ALL(x):[Set(x) => ALL(a):[a in x => a=a]]
> > Conclusion, 1
> >
> > Dan
> >
> > Download my DC Proof 2.0 freeware at http://www.dcproof.com
> > Visit my Math Blog at http://www.dcproof.wordpress.com

Maybe you have entered now the baby phase
that these behave similarly, since we have:

~ALL(a):[a e X] <=> EXIST(a):[~a e X]

How long will this baby phase last. Multiple
months? It only makes me marvel once again
whether you wrote DC proof by yourself.

Most likely you stole it, inherited it from someone
or got it by some other means. After all your
DC proof tools has these two inference rules:
- Quantifier switch (annoyingly introduces an extra negation sign)
- Double negation removal

So you should know quantifier duality of ALL and
EXIST sleep walking. But you are totally clueless and
extremly slow. That DC proof has many inference

rules that unnecessarely introduce a negation sign,
even if not necessary for classical logic, let me
already to the speculation that the real author

had some intuitionistic tool in mind, or that the present
author is an utter moron, who wants to terrorize the
users of DC proof by complete nonsense inference rules.

I am still undecided which of the stories behind DC proof
are true. Maybe both. When DC proof changed hands
nobody told the owner: Watch out intuitionistic inference

rules. And since the new owner doesnt know a damn
bit of intuitionistic logic, there is now this crank tool.

Mild Shock schrieb am Samstag, 3. Juni 2023 um 20:22:10 UTC+2:
> Also for a moron like you it might not be evident
> that you can replace a=a by TRUE. So you proved
> these two theorems:
>
> ~ALL(a):[a e X]
> TRUE
>
> The first theorem has not even a mosquito leg
> difference from your Universal Set theorem, at
> least not in classical logic. And the second theorem,
>
> is not something anybody would surprise.
> Mild Shock schrieb am Samstag, 3. Juni 2023 um 20:10:13 UTC+2:
> > I guess its rather the paradox of irrelevance.
> > There are so many theorens that are irrelevant,
> > und would never make it into a paper, since
> >
> > they use either inconsistent assumptions,
> > or then are non-construction and can therefore not be
> > applied. Are just some Unicorn dreams.
> >
> > Maybe post some math when have outgrown your
> > juvenile phase of 1000-th version of Russels paradox
> > which is totally irrelevant and useless to mathematics.
> > Dan Christensen schrieb am Samstag, 3. Juni 2023 um 19:36:20 UTC+2:
> > > Using ordinary set theory, we can prove:
> > >
> > > (1) ALL(a):[a in X & a=a] is FALSE for any set X.
> > >
> > > Whereas
> > >
> > > (2) ALL(a):[a in X => a=a]] is TRUE for any set X.
> > >
> > > ----------------------------------------------------------------------
> > > PROOF (1)
> > >
> > > Lemma: From Russel's Paradox (Proof: http://dcproof.com/UniversalSet.htm )
> > >
> > > 1. ALL(a):[Set(a) => EXIST(b):~b in a]
> > > Axiom
> > >
> > > Let x be a set
> > >
> > > 2. Set(x)
> > > Premise
> > >
> > > Apply lemma
> > >
> > > 3. Set(x) => EXIST(b):~b in x
> > > U Spec, 1
> > >
> > > 4. EXIST(b):~b in x
> > > Detach, 3, 2
> > >
> > > 5. ~y in x
> > > E Spec, 4
> > >
> > > 6. ~y in x | ~y=y
> > > Arb Or, 5
> > >
> > > 7. ~[~~y in x & ~~y=y]
> > > DeMorgan, 6
> > >
> > > 8. ~[y in x & ~~y=y]
> > > Rem DNeg, 7
> > >
> > > 9. ~[y in x & y=y]
> > > Rem DNeg, 8
> > >
> > > 10. ALL(x):[Set(x) => EXIST(a):~[a in x & a=a]]
> > > Conclusion, 2
> > >
> > > 11. ALL(x):[Set(x) => ~ALL(a):~~[a in x & a=a]]
> > > Quant, 10
> > >
> > > 12. ALL(x):[Set(x) => ~ALL(a):[a in x & a=a]]
> > > Rem DNeg, 11
> > >
> > > ----------------------------------------------------------------------
> > > PROOF (2)
> > >
> > > 1. Set(x)
> > > Premise
> > >
> > > 2. y in x
> > > Premise
> > >
> > > 3. y=y
> > > Reflex
> > >
> > > 4. ALL(a):[a in x => a=a]
> > > Conclusion, 2
> > >
> > > 5. ALL(x):[Set(x) => ALL(a):[a in x => a=a]]
> > > Conclusion, 1
> > >
> > > Dan
> > >
> > > Download my DC Proof 2.0 freeware at http://www.dcproof.com
> > > Visit my Math Blog at http://www.dcproof.wordpress.com

Or to put it simple, so that you understand why your tool
makes people dumb, including yourself. Your tool doesn't
provide de Morgan rules. You cannot do with one click:

~(A v B) ~~> ~A & ~B

https://en.wikipedia.org/wiki/De_Morgan%27s_laws

You meed many many clicks, one click that replaces the
logical connective, and introduces a hell of new negation
signs, and a couple of other clicks to remove the double

negations. Same problem with quantifiers.

P.S.: It also wrongly labels rules as de Morgan, but its
not de Morgan in the sense of classical de Morgan laws.
Its something else. Here is an example:

1 ~[P | Q]
Premise

2 ~~[~P & ~Q]
DeMorgan, 1

3 ~P & ~Q
Rem DNeg, 2

Mild Shock schrieb:
>
> Maybe you have entered now the baby phase
> that these behave similarly, since we have:
>
> ~ALL(a):[a e X] <=> EXIST(a):[~a e X]
>
> How long will this baby phase last. Multiple
> months? It only makes me marvel once again
> whether you wrote DC proof by yourself.
>
> Most likely you stole it, inherited it from someone
> or got it by some other means. After all your
> DC proof tools has these two inference rules:
> - Quantifier switch (annoyingly introduces an extra negation sign)
> - Double negation removal
>
> So you should know quantifier duality of ALL and
> EXIST sleep walking. But you are totally clueless and
> extremly slow. That DC proof has many inference
>
> rules that unnecessarely introduce a negation sign,
> even if not necessary for classical logic, let me
> already to the speculation that the real author
>
> had some intuitionistic tool in mind, or that the present
> author is an utter moron, who wants to terrorize the
> users of DC proof by complete nonsense inference rules.
>
> I am still undecided which of the stories behind DC proof
> are true. Maybe both. When DC proof changed hands
> nobody told the owner: Watch out intuitionistic inference
>
> rules. And since the new owner doesnt know a damn
> bit of intuitionistic logic, there is now this crank tool.

That your tool provides intuitionistic de Morgan is explained here:

Three out of the four implications of de Morgan's laws hold in
intuitionistic logic.
https://en.wikipedia.org/wiki/De_Morgan%27s_laws#In_intuitionistic_logic

The workaround for intuitionistic logic is then to use for example:

A v B ~~> ~(~A & ~B)

This is also detailed on Wikipedia.

Mild Shock schrieb:
> Or to put it simple, so that you understand why your tool
> makes people dumb, including yourself. Your tool doesn't
> provide de Morgan rules. You cannot do with one click:
>
> ~(A v B)   ~~> ~A & ~B
>
> https://en.wikipedia.org/wiki/De_Morgan%27s_laws
>
> You meed many many clicks, one click that replaces the
> logical connective, and introduces a hell of new negation
> signs, and a couple of other clicks to remove the double
>
> negations. Same problem with quantifiers.
>
> P.S.: It also wrongly labels rules as de Morgan, but its
> not de Morgan in the sense of classical de Morgan laws.
> Its something else. Here is an example:
>
> 1    ~[P | Q]
>     Premise
>
> 2    ~~[~P & ~Q]
>     DeMorgan, 1
>
> 3    ~P & ~Q
>     Rem DNeg, 2
>
> Mild Shock schrieb:
>>
>> Maybe you have entered now the baby phase
>> that these behave similarly, since we have:
>>
>> ~ALL(a):[a e X] <=> EXIST(a):[~a e X]
>>
>> How long will this baby phase last. Multiple
>> months? It only makes me marvel once again
>> whether you wrote DC proof by yourself.
>>
>> Most likely you stole it, inherited it from someone
>> or got it by some other means. After all your
>> DC proof tools has these two inference rules:
>> - Quantifier switch (annoyingly introduces an extra negation sign)
>> - Double negation removal
>>
>> So you should know quantifier duality of ALL and
>> EXIST sleep walking. But you are totally clueless and
>> extremly slow. That DC proof has many inference
>>
>> rules that unnecessarely introduce a negation sign,
>> even if not necessary for classical logic, let me
>> already to the speculation that the real author
>>
>> had some intuitionistic tool in mind, or that the present
>> author is an utter moron, who wants to terrorize the
>> users of DC proof by complete nonsense inference rules.
>>
>> I am still undecided which of the stories behind DC proof
>> are true. Maybe both. When DC proof changed hands
>> nobody told the owner: Watch out intuitionistic inference
>>
>> rules. And since the new owner doesnt know a damn
>> bit of intuitionistic logic, there is now this crank tool.

See my replies just now to your identical postings at sci.logic

Dan

On Saturday, June 3, 2023 at 3:14:35 PM UTC-4, Mild Shock wrote:
> That your tool provides intuitionistic de Morgan is explained here:
>
> Three out of the four implications of de Morgan's laws hold in
> intuitionistic logic.
> https://en.wikipedia.org/wiki/De_Morgan%27s_laws#In_intuitionistic_logic
>
[snip]

Do you need glasses? What on earth
makes you think that what I picked here:

~(A v B) ~~> ~A & ~B
https://en.wikipedia.org/wiki/De_Morgan%27s_laws

Is the same as this nonsense:

Dan Christensen schrieb am Samstag, 3. Juni 2023 um 21:25:26 UTC+2:
> 3. A | B => ~[~A & ~B]
> Conclusion, 1
https://groups.google.com/g/sci.logic/c/8F9_EdEOXa0/m/1oKmQttZBgAJ

Its NOT THE SAME . You were supposed to
prove ~[A | B] => [~A & ~B]

Whats wrong with you? Still not getting what the CLASSICAL
de Morgan laws are, and sticking to your INTUITIONISTIC FRINGE?

(Your own words)

Dan Christensen schrieb am Samstag, 3. Juni 2023 um 21:31:51 UTC+2:
> See my replies just now to your identical postings at sci.logic
>
> Dan
> On Saturday, June 3, 2023 at 3:14:35 PM UTC-4, Mild Shock wrote:
> > That your tool provides intuitionistic de Morgan is explained here:
> >
> > Three out of the four implications of de Morgan's laws hold in
> > intuitionistic logic.
> > https://en.wikipedia.org/wiki/De_Morgan%27s_laws#In_intuitionistic_logic
> >
> [snip]

I didn't say that your inference rules
are not valid. They are clumsy nonsense.

And they don't deserve the name they have.
You can check yourself, the deMorgan laws

are other laws, like for example:

~(A v B) ~~> ~A & ~B
https://en.wikipedia.org/wiki/De_Morgan%27s_laws

I don't know how to fix your dumbass tool.
You have to figure this out by yourself.

Good Luck!

Mild Shock schrieb:
> Do you need glasses? What on earth
> makes you think that what I picked here:
>
> ~(A v B) ~~> ~A & ~B
> https://en.wikipedia.org/wiki/De_Morgan%27s_laws
>
> Is the same as this nonsense:
>
> Dan Christensen schrieb am Samstag, 3. Juni 2023 um 21:25:26 UTC+2:
>> 3. A | B => ~[~A & ~B]
>> Conclusion, 1
> https://groups.google.com/g/sci.logic/c/8F9_EdEOXa0/m/1oKmQttZBgAJ
>
> Its NOT THE SAME . You were supposed to
> prove ~[A | B] => [~A & ~B]
>
> Whats wrong with you? Still not getting what the CLASSICAL
> de Morgan laws are, and sticking to your INTUITIONISTIC FRINGE?
>
> (Your own words)
>
> Dan Christensen schrieb am Samstag, 3. Juni 2023 um 21:31:51 UTC+2:
>> See my replies just now to your identical postings at sci.logic
>>
>> Dan
>> On Saturday, June 3, 2023 at 3:14:35 PM UTC-4, Mild Shock wrote:
>>> That your tool provides intuitionistic de Morgan is explained here:
>>>
>>> Three out of the four implications of de Morgan's laws hold in
>>> intuitionistic logic.
>>> https://en.wikipedia.org/wiki/De_Morgan%27s_laws#In_intuitionistic_logic
>>>
>> [snip]

The rules you implemented are even not part
of the square of opposition, nor part of de Morgan,
you implemented some replacement rules, the

balance of these rules is that they add two negation
signs, thats why they are clumsy:

/* Replacement Rules */
EXIST(x):A(x) ~~> ~ALL(x):~A(x)
ALL(x):A(x) ~~> ~EXIST(x):~A(x)

The square of opposition has these 4 rules,
the balance of these rules are that they remove
two negations, or keep the number of negations the same:

~EXIST(x):~A(x) ~~> ALL(x):A(x)
~ALL(x):~A(x) ~~> EXIST(x):A(x)
~EXIST(x):A(x) ~~> ALL(x):~A(x)
~ALL(x):A(x) ~~> EXIST(x):~A(x)
https://en.wikipedia.org/wiki/Square_of_opposition

Two of them are de Morgan. The de Morgan has these
4 rules. The balance of these rules is that they
always keep the number of negations the same:

ALL(x):~A(x) ~~> ~EXIST(x):A(x)
EXIST(x):~A(x) ~~> ~ALL(x):A(x)
~EXIST(x):A(x) ~~> ALL(x):~A(x)
~ALL(x):A(x) ~~> EXIST(x):~A(x)
https://en.wikipedia.org/wiki/De_Morgan%27s_laws

So you picked the worst inference rules, those
that add negation signs. Whereas for classical
logic there exist inference rules that remove

negation signs or keep the number of negation
signs constant. Well Shit Happens!

Mild Shock schrieb am Samstag, 3. Juni 2023 um 22:08:16 UTC+2:
> I didn't say that your inference rules
> are not valid. They are clumsy nonsense.
>
> And they don't deserve the name they have.
> You can check yourself, the deMorgan laws
>
> are other laws, like for example:
> ~(A v B) ~~> ~A & ~B
> https://en.wikipedia.org/wiki/De_Morgan%27s_laws
> I don't know how to fix your dumbass tool.
> You have to figure this out by yourself.
>
> Good Luck!
>
> Mild Shock schrieb:
> > Do you need glasses? What on earth
> > makes you think that what I picked here:
> >
> > ~(A v B) ~~> ~A & ~B
> > https://en.wikipedia.org/wiki/De_Morgan%27s_laws
> >
> > Is the same as this nonsense:
> >
> > Dan Christensen schrieb am Samstag, 3. Juni 2023 um 21:25:26 UTC+2:
> >> 3. A | B => ~[~A & ~B]
> >> Conclusion, 1
> > https://groups.google.com/g/sci.logic/c/8F9_EdEOXa0/m/1oKmQttZBgAJ
> >
> > Its NOT THE SAME . You were supposed to
> > prove ~[A | B] => [~A & ~B]
> >
> > Whats wrong with you? Still not getting what the CLASSICAL
> > de Morgan laws are, and sticking to your INTUITIONISTIC FRINGE?
> >
> > (Your own words)
> >
> > Dan Christensen schrieb am Samstag, 3. Juni 2023 um 21:31:51 UTC+2:
> >> See my replies just now to your identical postings at sci.logic
> >>
> >> Dan
> >> On Saturday, June 3, 2023 at 3:14:35 PM UTC-4, Mild Shock wrote:
> >>> That your tool provides intuitionistic de Morgan is explained here:
> >>>
> >>> Three out of the four implications of de Morgan's laws hold in
> >>> intuitionistic logic.
> >>> https://en.wikipedia.org/wiki/De_Morgan%27s_laws#In_intuitionistic_logic
> >>>
> >> [snip]

Mild Shock wrote:

> /* Replacement Rules */ EXIST(x):A(x) ~~> ~ALL(x):~A(x)
> ALL(x):A(x) ~~> ~EXIST(x):~A(x)

kiss my ass. You are Mostowske. A fucking nazi. Ukraine lost the war with
all his nazis. The idiots don't realize the capitalism and nazis are the
same thing. The capitalists supports the nazis, since the nazis, as
stupid, will fight to death for them. Similarly the nazis like the
capitalism, since the capitalists are feeding them, with products, others
just dream of. Once the nazis are dead, the capitalists lost the war,
since no human being will fight to death for the sake of the others,
wealthy capitalists.

You are assuming there are opposities nazi and ruski.
So I guess you accept ~nazi=ruski and ~ruski=nazi.
And therefore by substitution ~~nazi=nazi?

If you drop involution as a requirement, you might
end up with so called Ockham algebras. Which is
characterized by dual lattice endomorphism.

Somehow a fitting name, reference to Ockham
razor?, since it doesn't require much, except duality
in the form of de Morgan laws for meet and join,

but no de Morgan law for the function f, the
endomorphism. But you see that there is
only one negation:

f(a v b) = f(a) & f(b)
f(a & b) = f(a) & f(b)

And not two negations as here in Dan-O-Matik:

a v b = g(f(a) & f(b))
a & b = g(f(a) v f(b))

This could make a dent.

Heath Lucassen schrieb am Samstag, 3. Juni 2023 um 23:12:18 UTC+2:
> Mild Shock wrote:
>
> > /* Replacement Rules */ EXIST(x):A(x) ~~> ~ALL(x):~A(x)
> > ALL(x):A(x) ~~> ~EXIST(x):~A(x)
> kiss my ass. You are Mostowske. A fucking nazi. Ukraine lost the war with
> all his nazis. The idiots don't realize the capitalism and nazis are the
> same thing. The capitalists supports the nazis, since the nazis, as
> stupid, will fight to death for them. Similarly the nazis like the
> capitalism, since the capitalists are feeding them, with products, others
> just dream of. Once the nazis are dead, the capitalists lost the war,
> since no human being will fight to death for the sake of the others,
> wealthy capitalists.

Mild Shock wrote:

> but no de Morgan law for the function f, the endomorphism. But you see
> that there is only one negation: f(a v b) = f(a) & f(b)
> f(a & b) = f(a) & f(b)

The old Khazarian Kingdom with a Khazar in charge of it, little wonder why
all the "leaders", bankers and media are pushing for war with Russia, it
not only represents an opportunity to remake what was lost, but it has
also a symbolic meaning to the Non Semitic khazar goys. They are eating
pork and sniff cocaine. Deeply forbidden in The Bible.

If this dirty Flesenky clown empty his bank accounts in the Caiman islands
and other fiscal paradises, he would be able to pay it himself. Point is
that his money is stolen from the Ukraine civilians. The rest of the
politicians there are also corrupt! Civilians who are forced to be solder,
people with a family, he sends to the front because 1000 people more or
less doesn't mean anything to him. This man is evil, and he is a real
monster, but in fact the US is behind him. Unbelievable that a country not
belonging to the NATO and EU demand billions of dollars. Yes, and even
gets it! A country which is in the top 10 of the most corrupt countries in
the world. But his girlfriend (Ursula von der Leyen) who is so in love
with him makes it all happen, together with Borrel, Michel and so many
others who only dine in expensive restaurant and fly private jets. It is
one big mess, but the West will pay the price in the end.

https://r%74.com/ru%73%73ia/577421-kiev-demand-billion-weapons-west/

Not all equalitys are the same.
Some are the same by zero.
Some are the same by an infinitesimal.

Yeah, kill all ruskis with some nukes! This vermin
needs to be eradicated. The soon the better.

Herbert Vandale schrieb am Sonntag, 4. Juni 2023 um 00:04:20 UTC+2:
> all the "leaders", bankers and media are pushing for war with Russia, it

Thanks to the war, russians and ukrainians capacity and
experience in treating the wounded has dramatically increased:

https://twitter.com/vesloveselo/status/1665036830855634946

Soon their average life expectancy will increase dramatically.
What are the newest figures? In 2020 it was only:

• male 66.49 years
• female 76.43 years

https://en.wikipedia.org/wiki/Demographics_of_Russia

Mild Shock schrieb am Sonntag, 4. Juni 2023 um 02:08:42 UTC+2:
> Yeah, kill all ruskis with some nukes! This vermin
> needs to be eradicated. The soon the better.
> Herbert Vandale schrieb am Sonntag, 4. Juni 2023 um 00:04:20 UTC+2:
> > all the "leaders", bankers and media are pushing for war with Russia, it

Mathematically its also still possible that the low life
expantancy is an aftermath of the tourbulent years 1940-1946.
Now they do everything in 2022-2023 to keep this tradition.

Mild Shock schrieb am Sonntag, 4. Juni 2023 um 02:18:49 UTC+2:
> Thanks to the war, russians and ukrainians capacity and
> experience in treating the wounded has dramatically increased:
>
> https://twitter.com/vesloveselo/status/1665036830855634946
>
> Soon their average life expectancy will increase dramatically.
> What are the newest figures? In 2020 it was only:
>
> • male 66.49 years
> • female 76.43 years
>
> https://en.wikipedia.org/wiki/Demographics_of_Russia
> Mild Shock schrieb am Sonntag, 4. Juni 2023 um 02:08:42 UTC+2:
> > Yeah, kill all ruskis with some nukes! This vermin
> > needs to be eradicated. The soon the better.
> > Herbert Vandale schrieb am Sonntag, 4. Juni 2023 um 00:04:20 UTC+2:
> > > all the "leaders", bankers and media are pushing for war with Russia, it

See my reply just now to your identical posting at sci.logic.

Dan

On Saturday, June 3, 2023 at 4:08:16 PM UTC-4, Mild Shock wrote:
> I didn't say that your inference rules
> are not valid.

[snip]

On Sat Jun 3 15:04:15 2023 "mitchr...@gmail.com" wrote:
> Not all equalitys are the same.
> Some are the same by zero.
> Some are the same by an infinitesimal.

*
An exmple of the work of Mitchell's poetry.

Please do not read this as Science.

earle
*

Yes I know, that you don't care that your DC Proof
is utter nonsense. There is a lot of asymmetry in your
DC Proof which makes it doing proofs a pain in the ass.

Another example which is quite unfortunate is the
fact that you have only this rule:

(A <=> B) <~~> (A => B) & (B => A)

But this rule is missing:

(A <=> B) <~~> (A & B) v (~A & ~B)

Which makes it hard to prove something with negative
(A <=> B), like when (A <=> B) is on the lefthand side of (=>).
Try proving this simple propositional theorem:

(r <=> p) & (p <=> q) => (r <=> q)

How many lines? 100 hundred lines?

Dan Christensen schrieb am Sonntag, 4. Juni 2023 um 04:29:05 UTC+2:
> See my reply just now to your identical posting at sci.logic.
>
> Dan
> On Saturday, June 3, 2023 at 4:08:16 PM UTC-4, Mild Shock wrote:
> > I didn't say that your inference rules
> > are not valid.
> [snip]

Or maybe this one:

~ (p <=> q) <=> (p <=> ~q)

Mild Shock schrieb am Sonntag, 4. Juni 2023 um 15:48:12 UTC+2:
> Yes I know, that you don't care that your DC Proof
> is utter nonsense. There is a lot of asymmetry in your
> DC Proof which makes it doing proofs a pain in the ass.
>
> Another example which is quite unfortunate is the
> fact that you have only this rule:
>
> (A <=> B) <~~> (A => B) & (B => A)
>
> But this rule is missing:
>
> (A <=> B) <~~> (A & B) v (~A & ~B)
>
> Which makes it hard to prove something with negative
> (A <=> B), like when (A <=> B) is on the lefthand side of (=>).
> Try proving this simple propositional theorem:
>
> (r <=> p) & (p <=> q) => (r <=> q)
>
> How many lines? 100 hundred lines?
> Dan Christensen schrieb am Sonntag, 4. Juni 2023 um 04:29:05 UTC+2:
> > See my reply just now to your identical posting at sci.logic.
> >
> > Dan
> > On Saturday, June 3, 2023 at 4:08:16 PM UTC-4, Mild Shock wrote:
> > > I didn't say that your inference rules
> > > are not valid.
> > [snip]

DC Proof is a kind of a masochist version of a Proof
assistant/ Proof writing system. That it doesn't assume
that the domain is non-empty is the smallest problem.

Its very weak in propositional logic. Extremly annoying.

Mild Shock schrieb am Sonntag, 4. Juni 2023 um 15:49:10 UTC+2:
> Or maybe this one:
>
> ~ (p <=> q) <=> (p <=> ~q)
> Mild Shock schrieb am Sonntag, 4. Juni 2023 um 15:48:12 UTC+2:
> > Yes I know, that you don't care that your DC Proof
> > is utter nonsense. There is a lot of asymmetry in your
> > DC Proof which makes it doing proofs a pain in the ass.
> >
> > Another example which is quite unfortunate is the
> > fact that you have only this rule:
> >
> > (A <=> B) <~~> (A => B) & (B => A)
> >
> > But this rule is missing:
> >
> > (A <=> B) <~~> (A & B) v (~A & ~B)
> >
> > Which makes it hard to prove something with negative
> > (A <=> B), like when (A <=> B) is on the lefthand side of (=>).
> > Try proving this simple propositional theorem:
> >
> > (r <=> p) & (p <=> q) => (r <=> q)
> >
> > How many lines? 100 hundred lines?
> > Dan Christensen schrieb am Sonntag, 4. Juni 2023 um 04:29:05 UTC+2:
> > > See my reply just now to your identical posting at sci.logic.
> > >
> > > Dan
> > > On Saturday, June 3, 2023 at 4:08:16 PM UTC-4, Mild Shock wrote:
> > > > I didn't say that your inference rules
> > > > are not valid.
> > > [snip]

See my replies just now to your identical postings at sci.logic

Dan

On Sunday, June 4, 2023 at 9:48:12 AM UTC-4, Mild Shock wrote:
> Yes I know, that you don't care that your DC Proof
> is utter nonsense. There is a lot of asymmetry in your
> DC Proof which makes it doing proofs a pain in the ass.
>
> Another example which is quite unfortunate is the
> fact that you have only this rule:
>
[snip]

Omg. 60 Lines.

Currently you dont have any de Morgan for bi-implicaion.
You only have the one definition of bi-implication,
namely this one:

(A <=> B) <~~> (A => B) & (B => A)

You could prove it much quicker if you had de Morgan
for bi-implication. You can derive de Morgan for bi-
implication from this one:

(A <=> B) <~~> (A & B) v (~A & ~B)

The de Morgan is then:

~ (A <=> B) <~~> (~A v ~B) & (A v B)

You dont take duality in classical logic seriously Dan O Matik.
Your DC Proof is too much leaning towards intuitionistic
logic, or as you say the INTUITIONISTIC FRINGE.

Dan Christensen schrieb am Sonntag, 4. Juni 2023 um 18:43:57 UTC+2:
> See my replies just now to your identical postings at sci.logic
>
> Dan
> On Sunday, June 4, 2023 at 9:48:12 AM UTC-4, Mild Shock wrote:
> > Yes I know, that you don't care that your DC Proof
> > is utter nonsense. There is a lot of asymmetry in your
> > DC Proof which makes it doing proofs a pain in the ass.
> >
> > Another example which is quite unfortunate is the
> > fact that you have only this rule:
> >
> [snip]

See my reply just now to your identical posting at sci.logic

Dan

On Sunday, June 4, 2023 at 3:25:24 PM UTC-4, Mild Shock wrote:
> Omg. 60 Lines.
>
> Currently you dont have any de Morgan for bi-implicaion.
> You only have the one definition of bi-implication,
> namely this one:
> [snip]