['implies', 'if-then', 'only if', 'is a sufficient condition for']),
('Biconditional', ['<->', u'\u2261'], 'INFIX OP',
['if and only if', 'iff', 'just if']),
('Necessitation', ['N:', u'\u25A1'], 'PREFIX OP',
['it is necessary that', 'it is necessarilly the case that']),
('Possibility', ['P:', u'\u25C7'], 'PREFIX OP',
['it is possible that', 'it is possibly the case that']),
('Entailment', ['|-', u'\u22A6'], 'ENTAILS', ['entails'])
]
GentzenLanguage = Language(GentzenLexicon, ['<->', u'\u2261'])
GentzenRules = [
# Name Abbreviation Form (Sequent)
# ============================== ============ =============================================
('Given', 'Given', GentzenLanguage.parseSeq(' |- P')
),
('Modus Ponens', 'MP',
GentzenLanguage.parseSeq('P > Q, P |- Q')),
('Modus Tollens', 'MT',
GentzenLanguage.parseSeq('P > Q, ~Q |- ~P')),
('Hypothetical Syllogism', 'HS',
GentzenLanguage.parseSeq('P > Q, Q > R |- P > R')),
('Disjunctive Syllogism 1', 'DS1',
GentzenLanguage.parseSeq('P v Q, ~P |- Q')),
('Disjunctive Syllogism 2', 'DS2',
GentzenLanguage.parseSeq('P v Q, ~Q |- P')),
('Constructive Dilemma', 'CD',
GentzenLanguage.parseSeq('P v Q, P > R, Q > S |- R v S, S v R')),
('Absorption', 'Abs',
GentzenLanguage.parseSeq('P > Q |- P > (P & Q)')),
