Sequent calculus

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Problem: Prove the admissibility of the rule. \[ \frac{\Gamma, A \vdash C, \Gamma, B \vdash C}{\Gamma, A \vee B \vdash C} . \]

6.1.2.1 Sequent calculus

1.53 $

Problem: Construct a derivation of sequence in sequent calculus: \[ (\varphi \rightarrow \psi),(\psi \rightarrow x) \vdash(\varphi \rightarrow x) . \]

6.1.2.2 Sequent calculus

2.55 $

Problem: Prove the derivability of the formula in sequent calculus: \[ \vdash(\overline{A \cdot \bar{B}}) \rightarrow(A \rightarrow B) . \]

6.1.2.3 Sequent calculus

1.53 $

Problem: Prove the derivability of the formula in sequent calculus: \[ \vdash A(\bar{B} \vee C) \rightarrow(A \bar{B} \vee C) \text {. } \]

6.1.2.4 Sequent calculus

1.78 $

Problem: Prove the derivability of the formula in sequent calculus: \[ \vdash(A \rightarrow B) \vee(C \rightarrow B) \rightarrow(A C \rightarrow B) . \]

6.1.2.5 Sequent calculus

1.78 $

Problem: Prove the derivability of the formula in sequent calculus: \[ \vdash \overline{A \vee B} \rightarrow(\mathrm{A} \rightarrow \bar{B}) . \]

6.1.2.6 Sequent calculus

1.53 $