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Theorem 4.112 and 4.72 are now separated into two distinct statements.

Lemmas 4.115 and 4.73 are now separated into two distinct statements.

Proof of theorem 4.137: Last paragraph modified.

Proposition 4.140: Added the word “distributive”.

Theroem 4.142: Strenghtened: atomistic

atomic.

Proof of theorem 4.144: 1.

X →

up

X

. 2. proof clairified.

Proof of theorem 4.150: Added: “Core part and dual core part are defined because the core is a
complete lattice.”

Proof of proposition 4.159:

=

→ ∼

.

Proof of proposition 4.161:

A

Z

.

Proposition 4.178: max

a

max down

a

.

Proposition 4.184: Removed

S

P

F

\ {∅}

.

Proof of lemma 4.231: Removed “

X

”.

Corollary 3.232:

G → A

.

Proof of theorem 4.233:

X

card

X

.

Proof of example 4.235:

x

=

{

a,

1

} →

up

x

=

{

x, a,

1

}

.

Proposition 4.247:

S

[

S

]

.

Proposition 5.14: “

a

” removed.

Proposition 5.21:

.

Proof of proposition 5.33:

X

U

.

6.1 Informal introduction into funcoids:

α

β

.

Proposition 6.13: Strenghtened (removed the word “small”).

Proof of proposition 6.16:

β

1

β

2

.

Proof of theorem 6.27: 1.

Y

P

B

X

P

A

. 2.

a

α

.

Theroem 6.31: funcoids

funcoid.

Proof of lemma 6.33:

B

∈ h

F

i

X

B

FCD

(

Src

f

;

Dst

f

)

F

B

X

.

Proof of lemma 6.34:

X

→ X

.

Proof of theorem 6.36: Refer to a less general proposition (4.189).

Added remark 6.40.

Before theorem 6.42:

f

g

.

Proof of theorem 6.60: corollary 4.126

proposition 4.197.

Theorem 6.61:

A

B

.

Proof of theorem 6.61: 1.

α

α

. 2.

⊔ → ∪

. 3,

A

B

.

Proposition 6.67:

=

→ ⊑

.

Proof of theorem 6.74: Forgotten

X

.

Proof of theorem 6.96:

Y

→ ↑

B

Y

.

Proof of theorem 6.111:

f

g

.

2