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Conditional proofs
When mathematicians want to establish a conditional statement
, they add the hypothesis
to the set of their current working assumptions
,
and proceed to derive the desired conclusion
. When
the derivation of
is complete,
ceases to be
an active assumption--it is ``discharged''.
Note that the discharge is not explicitly made; mathematicians
do not say ``and now we discharge
.'' Rather, the
scope of the hypothesis
is lexically
apparent by the division of the proof text into units
such as paragraphs.
Conditional reasoning as described above is captured in
NDL by proofs of the form assume
. To
evaluate such a proof in an assumption base
,
we add the hypothesis
to
and proceed
to evaluate the body
in the augmented assumption
base
. Once we obtain a conclusion
, we return the implication
as the final result:
As a simple example, here is a proof of A ==> A:
assume A
claim A
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2004-08-06