eolas/Logic/Proofs/Disjunction_Introduction.md

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Logic

Disjunction Introduction

This rule can seem a little odd: like we are randomly introducing an additional proposition without giving any justification. However this is just a consequence of the fact if P is true, so is P \lor Q since disjunction is not the same as conjunction: only one disjunct needs to be true for the compound disjunction to be true. This is represented in the context of truth-trees by the fact that truth can pass up via either branch of a disjunction pattern. This rule is sometimes also referred to (confusingly) as Addition.