Ein pragmatisierter Kalkul des naturlichen Schlieβens nebst Metatheorie

154 3 Der Redehandlungskalkul

е) VANS(F)N) =

VANS(F)N+1) и {(max(Dom(VANS(⅛ti))), ⅛maχ(Dom(VANs(⅛r*))))},

f) VER(F) N)WER(F) N⁺1) ⊂ {A(⅛) I max(Dom(VANS(F)N))) ≤j<i},

g) VER(F)N) ⊂ {A(F)₇) I j ∈ Dom(VERS(F)N⁺I)N)) ^u

{ A(F)₇) I max(Dom(V ANS(F)N))) ≤ j < і},

h) VAN(F) N)W AN(F)N⁺I) C {A(⅛_max(Dom(VANS(⅛rs))))},

і) VAN(F)N) = VAN(F)N+1) и {A(F)_max(Dom(VANS(⅛∙))))} ^und

j) A(F),;) = ^l"A(F)_max(Dom(VANS(55rθ))) ^-* A(F),;.!)"¹

oder

(iii) F) N⁺1 ∈ NEF(F)N) und

a) {(j, F)₇) I max(Dom(VANS(F)N))) ≤j≤i} isteinNE-geschlossener Abschnitt
in F)N+1,

b) VERS(F)N)∖VERS(F)N+l) ⊂ {(j, F)₇) ∣ max(Dom(VANS(F)N))) ≤ j < i},

c) VERS(F)N+!) =

(VERS(F)N)∖{0, F)₇) I max(Dom(VANS(F)N))) ≤ j < i}) и {(( F),)},

d) VANS(F)N)WANS(F)N+l) = {(max(Dom(VANS(F)N))), F)_max(Dom(VANS(^)))},

e) VANS(F)N) =

VANS(F)N+1) и {(max(Dom(VANS(F)N))), F)_max(Dom(VANs(r>r∕))))},

f) VER(F) N)WER(F)N+1) ⊂ {A(F)₇) ∣ maχ(Dom(V ANS(F)N))) ≤j<i},

g) VER(F)N) C {A(F),) I j ∈ Dom(VERS(F)N⁺I) N)} и

{A(F)₇) I max(Dom(VANS(F)N))) ≤ j < i},

h) VAN(F)N)WAN(F)N÷1) C {A(⅛_max(D_0m(VANS(⅛rs))))},

i) VAN(F)N) = VAN(F)N⁺U и {A(F)_max(D_0m(VANS(⅛∙))))} ^und

j) A(F),;) A(F)_max(D_om( VA NS(5}∣z))))

oder

(iv) F)N+1 ∈ PBF(F)N) und

a) {(j, F)₇) I max(Dom(VANS(F)N))) ≤j≤i} istein PB-geschlossener Abschnitt
in F)N+1,

b) VERS(F)N)WERS(F)N+1) ⊂ {0', F)₇) ∣ max(Dom(VANS(F)N))) ≤ j < i},

c) VERS(F)N⁺U =

(VERS(F)N)W, F)₇) I max(Dom(VANS(F)N))) ≤ j < i}) и {(i, F),)},

d) VANS(F)N)WANS(F)N÷l) = {(max(Dom(VANS(F)N))), F)_max(D₀m(VANS(^)))},

e) VANS(F)N) =

VANS(F)N+1) и {(max(Dom(VANS(F)N))), F)_max(Dom(VANs(r>r∕))))},

f) VER(F)N)WER(F)N+1) ⊂ {A(⅛) ∣ max(Dom(VANS(F)N))) ≤j<i},

g) VER(F)N) C {A(F) ,) I j ∈ Dom(VERS(F)N⁺I) N)} и

{A(F)₇) I max(Dom(VANS(F)N))) ≤ j < i},

h) VAN(F) N)WAN(F) N⁺1) C {A(⅛_max(D_0m(VANS(⅛rs))))},