CM1 Flashcards
1
Q
LJ ax
A
________
Γ, A ⊢ A
2
Q
LK ax
A
________
Γ, A ⊢ Δ, A
3
Q
LJ cont
A
Γ, A, A ⊢ Δ
____________
Γ, A ⊢ Δ
4
Q
LK contright
A
Γ ⊢ Δ, A, A
____________
Γ ⊢ Δ, A
5
Q
LK contleft
A
Γ, A, A ⊢ Δ
____________
Γ, A ⊢ Δ
6
Q
LJ ⊤right
A
_______
Γ ⊢ ⊤
7
Q
LK ⊤right
A
_______
Γ ⊢ Δ, ⊤
8
Q
LJ ⊥left
A
_________
Γ, ⊥ ⊢ Δ
9
Q
LK ⊥left
A
_________
Γ, ⊥ ⊢ Δ
10
Q
LJ ¬right
A
Γ, A ⊢
________
Γ ⊢ ¬A
11
Q
LK ¬right
A
Γ, A ⊢ Δ
________
Γ ⊢ Δ, ¬A
12
Q
LJ ¬left
A
Γ ⊢ A
__________
Γ, ¬A ⊢ Δ
13
Q
LK ¬left
A
Γ ⊢ A, Δ
__________
Γ, ¬A ⊢ Δ
14
Q
LJ ∧right
A
Γ ⊢ A | Γ ⊢ B
________________
Γ ⊢ A ∧ B
15
Q
LK ∧right
A
Γ ⊢ Δ, A | Γ ⊢ Δ, B
________________
Γ ⊢ Δ, A ∧ B
16
Q
LJ ∧left
A
Γ, A, B ⊢ Δ
_______________
Γ, A ∧ B ⊢ Δ
17
Q
LK ∧left
A
Γ, A, B ⊢ Δ
_______________
Γ, A ∧ B ⊢ Δ