Testing...

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After Frouck! Mrouck!

Nic

Additive and &
Additive or ⊕ ⊕
Multiplicative and ⊗ ⊗
Multiplicative or ⅋ ⅋
Class. conjuction ∧ ∧
Top ⊤ ⊤
Class. disjunction ∨ ∨
Bottom ⊥ ⊥ ⊥
Linear implication ⊸ ⊸ ⊸ ⊸

Dashv : $\dashv$ and vdash $\vdash$

Afaiblissement $$ \frac{\Gamma \vdash \Delta}{A, \Gamma \vdash \Delta} $$ Contraction $$ \frac{A, A,\Gamma \vdash \Delta}{A, \Gamma \vdash \Delta} $$ Classical logic : $A \Rightarrow B \equiv \neg A \vee B$

Lin. imp: $A \multimap B \equiv A^\bot \parr B$

Cut rule $$\frac{\Gamma \vdash A \quad\quad A, \Delta \vdash B}{\Gamma, \Delta \vdash B} $$