The logic of proofs LP was introduced in [3] and thoroughly studied in [1]. LP
is a natural extension of the propositional calculus in the language representing
proofs as formal objects. Proof expressing terms are constructed using constants,
variables, and signs of natural operations on derivations. Then formula
t:F has the intended interpretation "t is a proof of F". LP is complete with
respect to the interpretation of t:F in the Peano arithmetic by an arithmetical
formula "t is a PA-derivation of F"
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