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∀#∪ ∨? ⓒ⇒⊂Rⓒ?

♣R∪∧TM ∨I ?

&ΦΦ

∀#∪ ∨? ⓒ⇒⊂Rⓒ?

♣R∪∧TM ∨I ?

&Ν

∀#∪ ∨? ⓒ⇒⊂Rⓒ?

♣R∪∧TM ∨I ?

&ΦΦ

∈?∪

&Υ

∀#∪ ∨? ⓒ⇒⊂Rⓒ?

♣R∪∧TM ∨I ?

&Υ

∈?∪

&ΦΦ

13

⊂#??∨ ⊂?∧∪∈?

↓?∨?∈∧?∨∪⇔∧∪∈?

Υ ∈∧R∨∪ⓒ

♣R∪∧TM ∨I ?

∂?∧ ⇔∧R

∧TM

∈TM ⊂#

% ∧⇒⊂?∧?

Υ ∈∧R∨∪ⓒ

♣R∪∧TM ∨I ?

I∪?

ⓒ?

∨ ?⊂ ⇔R∧R

∧?ⓒ

∨?

#TM

?G?R∧R

ⓒ?

⇔∧?⊂?∧ ⇔R∪

? ∧⇒⊂?∧?

?

⊂TMⓒ? ?.

&

↓∨TMⓒTM ∪?∈⇒#∧?

#∨TMI∨?⊂⊂?∧ R∧?∪

⊂R

⊂?∧?

)

∨?

#?∧ⓒ∧?

∧TM

∈TM ⊂#

% ∧⇒⊂?∧?

Υ ∈∧R∨∪ⓒ

♣R∪∧TM ∨I ?

)

G

7

⊇TM∨G .

(

Υ ∈∧R∨∪ⓒ ♣R∪∧TM ∨I ?

∪?∧ ?R∧?∪

?#⇒

)

G

7

⊇TM∨G .

°∪?

ⓒ?

????⊆R∧R

∧?

↓∨TMⓒ∪∈

∪?∨∈R∪?

⊂R

⊂?∧?

)

∨?

#?∧ ⇔∧R

∧TM

∈TM ⊂#

% ∧⇒⊂?∧?

Υ ∈∧R∨∪ⓒ

♣R∪∧TM ∨I ?

⇔∧∨G⊇TMⓒ∧?

∧TM

#∨TM

∧TM

∈?∪⊂?∧∪⇔∧∪∈⇒

⊂?↓?ⓒ?⊂?.

∝R ?∪ ?R ∧R

⇒∧∪

?ⓒ? R∪

∧TM

ΛΕΔ

(⊇ ∧?∈∪)

% ∧⇒⊂?∧?

Υ ∈∧R∨∪ⓒ

♣R∪∧TM ∨I ? .

°∪?

ⓒ?

?∈ ∨⇔R∧R

∧?

Υ ∈∧R∨∪ⓒ

♣R∪∧TM ∨I ?

#?∧ ⇔∧R

∧TM

∈TM ⊂#

% ∧⇒⊂?∧?

Υ ∈∧R∨∪ⓒ

♣R∪∧TM ∨I ?

∈?⊂#TM⇔R

⊇TM∨G

⊂G↓∨∪

∧TM

?⇔∧G∨∪

( )

ⓒ?

R⊆?⊇?ⓒ∪⇔∧R

?#⇒

∧?ⓒ

TM?⇒ⓒ?

?R∪∧TM ∨I ? .

∃♠!∀ ∃

:

∀

Υ ∈∧R∨∪ⓒ

♣R∪∧TM ∨I ?

TM ?R R∪

⊂R

∃ °∀

∧?↓ ∧?∧?

?ⓒR⊂∪⇔∧ ∨?

( ⊆?)

⊂R

⊂G∧∨∪?

∧?↓ ∧?∧?

?ⓒR⊂∪⇔∧ ∨?

(⊂R

?ⓒ∧? ?

?R∨⊂⇒∧?∧?

⊂⇒ⓒTM)

I∪?

⇔ ↓TM

#ⓒTM.

♠!

)∃

♣!∀)#? °∀∋

? ∃

:(

?R∨⊂TM∈∨?⇔ ?

?ⓒR ? ⓒR∪

? ∧⇒⊂?∧?

∈?∧?

)

?Χ

∧?

R#⇒⊂Rⓒ?

30

?R#∧?

∈?∪

∈?∧?

2

?Χ

∧?ⓒ

R#⇒⊂Rⓒ?

⊂ ?

∨?

I∪?

?ⓒR∧TM

#ⓒTM.

?⊂∪⇔?

?∨?

(

∨?

⊂#TM∨R

ⓒ?

∨ ?⊂∪⇔∧R

⊂⇒ⓒTM

?⊇TM

#?∧ ⇔R∧R

∧TM

∈TM ⊂#

♠? Rⓒ∪⇔⊂TM .

%ⓒ

G↓R∧R

⊂⇒?∪

????⊆R∪

⊂#?∧?∨ R

∧TM

∈TM ⊂#

♠? Rⓒ∪⇔⊂TM

??

#∨G#R∪

ⓒ?

#?∧??R

I∪?

ⓒ?

⊆?ⓒ?∨ ?⊂ ⇔R∧R

∧?ⓒ

∨?.

∂?∧ ⇔∧R

∧TM

∈TM ⊂#

ⓒ?∨⊆? /∂? ⇔?

♣R∪∧TM ∨I ? .

∂?∧ ⇔∧R

∧TM

(TM ⊂%

2νδ

Φ

∈?∪

R?GI ∧R

?ⓒ

?ⓒ? R∪

∧TM

R∪∈TMⓒ ∪TM

∧TM

(TM ⊂%∪TM

2νδ

Φ.

∂?∧ ⇔∧R

∧?

∈TM ⊂#∪?

?⊂∪⇔?

?∨?

⊂G↓∨∪

ⓒ?

∨ ?⊂ ⇔R∧R

∧?ⓒ

∨?

#TM

?G?R∧R.

∂?∧ ⇔∧R

∧TM

∈TM ⊂#

?≤♠∋ (

?∨TMⓒTM ∪?∈⇒#∧?.

(♠∀∋ (

:

∀?GI⊆∧R

∧TM

R ∈∧?

I∪?

#.⊂.

∈?∪

⊂.⊂.

∝R ?∪ ?R ∧R

⇒∧∪

?

∨?

G↓R∪

∨ ?⊂∪⇔∧R

⇔ ⇔∧?

⇔∧?ⓒ

TM?⇒ⓒ?

∧TM

∧??R↓R∪∨∪⇔∧?∨ TM .

∂?∧ ⇔∧R

∧TM

(TM ⊂%

2νδ

Φ

∂?∧ ⇔∧R

∧?

∈TM ⊂#∪?

%ⓒTM∪∈∧⇒/!?R∪⇔∧⇒

(ΟΝ/ΟΦΦ)

∧TM

?∨TMⓒTM ∪?∈⇒#∧?

I∪?

ⓒ?

?ⓒTM ⊆R∧R

ⓒ?

∈?R ⇔R∧R

∧TM

?∨TMⓒTM ∪?∈⇒#∧?.

∂?∧ ⇔∧R

∧?

∈TM ⊂#∪?

?⊂∪⇔?

?∨?

⊂G↓∨∪

ⓒ?

∨ ?⊂ ⇔R∧R

∧?ⓒ

∨?

#TM

?G?R∧R.

°∪?

ⓒ?

∈?ⓒTMⓒ ⇔R∧R

∧?ⓒ

R#∪?RI⊂Gⓒ?

∨?,

#?∧ ⇔∧R

∧TM

∈TM ⊂#

ΣΕΤ

( ?≤♠∋ ()

?∨TMⓒTM ∪?∈⇒#∧?.

°∪?

ⓒ?

?∈ ∨⇔R∧R

∧?

∨ ?⊂∪⇔?

∧TM

↓∨TMⓒTM ∪?∈⇒%∧?.

∀?GI ∧R

?ⓒ

R ⓒ?∪

⇔ ?⇔∧⇒

∧TM

R∪∈TMⓒ ∪TM

∧TM

(TM ⊂%∪TM

2νδ

Φ.

∂?∧ ⇔∧R

∧TM

∈TM ⊂#

%∈ ∨ ⇔?

?∨TMⓒTM ∪?∈⇒#∧?

Rⓒ

⇔∧TM↓R R∧R

∧TM

⇔?⊂?∧TM? #∧?

⊂R

∧TM

∧??R↓R∪∨∪⇔∧ ∨∪TM.

(∃TM

Rⓒ R∪∈∧∪∈⇒

??⊂#?∈∪

↓∨TMⓒTM ∪?∈⇒#∧?

∧TM

⊂?↓?ⓒ ⊂?∧TM

∈?∪

?

TM?⇒ⓒ?

⇔ ⓒTM ⓒ).

ⓒ?∨⊆?

)#∪ ∨? ⓒ⇒⊂Rⓒ?

♣R∪∧TM ∨I ? /∃∈ ∨ ⇔?

∂∨TM∨ ?⊂∪⇔?

∀♠)( ∀

:

)#∪?G⊆∧R

Gⓒ?

?#⇒

∧TM

#?∨?∈?∧

∧G⇔⇔R∨∪

∧∨⇒#TM

?R∪∧TM ∨I ? .

1

1

2

3

4

2

3

⊂R

∧TM

⊂?↓?ⓒ?⊂?

⇔R

?R∪∧TM ∨I ?

1

2

3

4

5

ON

OFF

CANCEL

SET

CANCEL

SET

CANCEL

ET

GREEK

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