Formal proofs with identity
Whereas informal proofs may be done in a variety of ways, depending on the level of
precision demanded by the audience at which the proof is aimed, the formal proofs we
will do will all follow the same format.
P
Q
R
S
1
Justification 1
:
:
S
n
Justification n
S
Justification n + 1
We will use a Fitchstyle system which places the premises of the argument above the
Fitch bar and the conclusion and all supporting steps below the Fitch bar.
Notice that to
the right of each supporting step, a justification must be given.
The reason such
justification is necessary is that a rule must be cited in order to add each new step to a
proof.
If each supporting step in the proof is justified by a correct usage of a rule, then
we can be certain that each step, including the conclusion, is a logical consequence of the
given premises.
Identity Introduction (= Intro):
n = n
The first rule we will use is
Identity Introduction
.
Like its informal counterpart, which
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 Fall '06
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 Logic, Fitch bar, Identity Introduction, Identity Elimination

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