Next: Conditional proofs
Up: Proof semantics
Previous: Rules dealing with equality
  Contents
Composite proofs
Composite proofs are used to link together multiple inference steps
in such a way that the conclusions of earlier deductions become
available in subsequent deductions. Specifically, to evaluate a
composite proof
in some assumption base
, we first evaluate
in
, obtaining some conclusion
; and we then evaluate
in the augmented assumption base
.
This means that the conclusion of
becomes available (serves as a ``lemma'')
inside
. The conclusion
we obtain by evaluating
in
becomes the
conclusion of the entire composition
. This is formally
specified as follows:
As an example, suppose we have the premise and
we want to derive the conclusion C. This can be done in three
steps: first we use right-and to obtain , then
we use right-and again to obtain , and finally
we use double-negation to get C. These three steps
can be put together using the semi-colon proof-composition
operator:
right-and A & B & ~~C; // this puts B & ~~C in the a.b.
right-and B & ~~C; // this puts ~~C in the a.b.
double-negation ~~C // and finally we get C
Note that the convention that ; associates to the right
is important in parsing the above deduction correctly.
Next: Conditional proofs
Up: Proof semantics
Previous: Rules dealing with equality
  Contents
2004-08-06