[SOLVED] R Proof Checking

Proof Checking
Language and Logic

p : P interpreted as p is a proof of P
p : P -> Q is furthermore interpreted as
p is a rule for converting a proof of P into a proof of Q.

The language of propositions revisited
Truth Falsity P, Q, P and Q P or Q P -> Q
not P = P -> Falsity
Proofs are created via rules.

Postulates: and-elimination

Postulates: and-introduction

Postulates: or-introduction

Postulates: or-elimination

Postulates: falsity-elimination

Postulates: double-negation-elimination

Postulates

Modus ponens

P, Q, R : P (Q R)

PQ : QP

PQ , QR : R

P, P Q : P (Q R)

P (Q R) : P Q

P (QR) : Q(P R)

P(QR), S : (SP)Q

QP : (PQ)

P Q, Q : P

P Q, P R, S Q : R S

Online installation: http://bit.ly/2ID3jN6