This is the Lecture Note

Exercise 1 [2 points) Prove the case involving VE of the inductive step of the strong) soundness theorem for natural deduction in classical propositional logic (see notes of Lecture 14 on OWL). Hint: you need to simultaneously consider 3 different instances of entailment, 1 regular and 2 featuring the transformation of an assumption into a premise. (Strong) soundness INDUCTIVE STEP: suppose that, for any R and A, if REA with a proof of size n, then REA (IH). We want to prove that if S E B with a proof of size n+1, then SEB. Case 8: the step n+1 is obtained via vE. Exercise 1 [2 points) Prove the case involving VE of the inductive step of the strong) soundness theorem for natural deduction in classical propositional logic (see notes of Lecture 14 on OWL). Hint: you need to simultaneously consider 3 different instances of entailment, 1 regular and 2 featuring the transformation of an assumption into a premise. (Strong) soundness INDUCTIVE STEP: suppose that, for any R and A, if REA with a proof of size n, then REA (IH). We want to prove that if S E B with a proof of size n+1, then SEB. Case 8: the step n+1 is obtained via vE