Sub-proofs, strategy, logical truth
Subproofs
:
Many of the proofs we will consider will require the use of sub-proofs. The reason that
subproofs are helpful, and sometimes necessary, is that the consideration of hypothetical
cases can lead you to steps in the proof that would be difficult to get otherwise.
When should sub-proofs be used?
At this point in the course, with only formal rules for the Boolean connectives and the
identity symbol, there are only a few specific cases in which sub-proofs will be needed.
•
∨
Elim
(proof by cases)
Applying the
∨
Elim
rule will always require the use of sub-proofs. If you
see that one of your premises is a disjunction, it is likely that you will need to
build sub-proofs so that you can eventually apply
∨
Elim
to the disjunction.
•
¬
Intro
(indirect proof)
Like
∨
Elim
, applying the
¬
Intro
rule will always require the use of
subproofs. If you see that your desired conclusion is a negated statement, or it
contains material not found in your premises, then it is likely that sub-proofs

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