Page 26 - MATINF Nr. 4

26 D. Constantin, A.F. S , tefan

5. ∂T = {n 5 , n 6 , n 2 } ; n = n 6 ; formula selectat˘a (β ∨ γ) ; se aplic˘a regula G7;

n 7
↑
n 5 n 6
↑ ↑
T : n 3 n 4
-%

n 1 n 2
-%
r

ϕ (n 7 ) = {α, β} =⇒ {β, γ} este secvent axiom˘a.
6. ∂T= {n 5 , n 7 , n 2 } ; n = n 2 ; formula selectat˘a ((¬α) → γ) ; se aplic˘a regula G4;

n 7
↑
n 5 n 6
↑ ↑
T : n 3 n 4 n 8 n 9
-% -%

n 1 n 2
-%
r

ϕ (n 8 ) = {γ} =⇒ {α, (β ∨ γ)} , ϕ (n 9 ) = Ø =⇒ {(¬α) , α, (β ∨ γ)}.
7. ∂T = {n 5 , n 7 , n 8 , n 9 } ; n = n 8 ; formula selectat˘a (β ∨ γ) ; se aplic˘a regula G7;

n 7
↑
n 5 n 6 n 10
↑ ↑ ↑

T : n 3 n 4 n 8 n 9
-% -%

n 1 n 2
-%
r

ϕ (n 10 ) = {γ} =⇒ {α, β, γ} este secvent axiom˘a.
8. ∂T = {n 5 , n 7 , n 10 , n 9 } ; n = n 9 ; formula selectat˘a (¬α) ; se aplic˘a regula G5;

n 7
↑
n 5 n 6 n 10 n 11
↑ ↑ ↑ ↑

T : n 3 n 4 n 8 n 9
-% -%
n 1 n 2
-%
r

ϕ (n 11 ) = {α} =⇒ {α, (β ∨ γ)} este secvent axiom˘a.