Discrete Mathematics
... A propositional variable (lowercase letters p, q, r) is a proposition. These variables model true/false statements. The negation of a proposition P, written ¬ P, is a proposition. The conjunction (and) of two propositions, written P ∧ Q, is a proposition. The disjunction (or) of two propositions, wr ...
... A propositional variable (lowercase letters p, q, r) is a proposition. These variables model true/false statements. The negation of a proposition P, written ¬ P, is a proposition. The conjunction (and) of two propositions, written P ∧ Q, is a proposition. The disjunction (or) of two propositions, wr ...
A SHORT AND READABLE PROOF OF CUT ELIMINATION FOR
... number (Definition 2.1) of the last rule applied in deriving (Γ ⊢ ∆)[a]. (2) (Γ ⊢ ∆)[a] = Γ[a], A[a] → B[a] ⊢ ∆[a]. Thus the premises of the rule,8 Γ[a], A[a] → ⊥ ⊢ ∆[a] and Γ[a], B[a] ⊢ ∆[a], are each derived with orders < m. By the I.H., Γ[b], A[b] → ⊥ ⊢ ∆[b] and Γ[b], B[b] ⊢ ∆[b] are derived with ...
... number (Definition 2.1) of the last rule applied in deriving (Γ ⊢ ∆)[a]. (2) (Γ ⊢ ∆)[a] = Γ[a], A[a] → B[a] ⊢ ∆[a]. Thus the premises of the rule,8 Γ[a], A[a] → ⊥ ⊢ ∆[a] and Γ[a], B[a] ⊢ ∆[a], are each derived with orders < m. By the I.H., Γ[b], A[b] → ⊥ ⊢ ∆[b] and Γ[b], B[b] ⊢ ∆[b] are derived with ...