Documentation

Foundation.Logic.Disjunctive

class LO.System.Disjunctive {F : Type u_1} [LO.LogicalConnective F] {S : Type u_2} [LO.System F S] (𝓢 : S) :
Instances
    theorem LO.System.Disjunctive.disjunctive {F : Type u_1} [LO.LogicalConnective F] {S : Type u_2} [LO.System F S] {𝓢 : S} [self : LO.System.Disjunctive 𝓢] {p : F} {q : F} :
    𝓢 ⊢! p q𝓢 ⊢! p 𝓢 ⊢! q
    theorem LO.System.iff_disjunctive {F : Type u_1} [LO.LogicalConnective F] {S : Type u_2} [LO.System F S] {𝓢 : S} :
    LO.System.Disjunctive 𝓢 ∀ {p q : F}, 𝓢 ⊢! p q𝓢 ⊢! p 𝓢 ⊢! q