[SOLVED] 代写 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)

P⋀Q : Q⋀P

P⋀Q , Q→R : R

¬¬P, P → Q : P ∧ (Q ∨ R)

P → (Q ∧ R) : P → Q

P →(Q→R) : Q→(P →R)

P∨(Q∧R), S : (S∧P)∨Q

Q→¬P : ¬(P∧Q)

¬P → Q, ¬Q : P

P ∨ Q, P → R, S → ¬Q : R ∨ ¬S

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