Attempt to prove using contradictory hypotheses
fh(h)
with:
this command enables to perform a demonstration, by proving that a hypothesis is contradictory to the others.
If
the
lemma
to
be
demonstrated
is
G
under
the
hypotheses
h1
,
…
,
hn
and
the
user
suspects
that
one
of
the
hypotheses
hi
is
contradictory
to
the
others,
we
can
demonstrate
the
lemma
by
demonstrating:
¬hi under the hypotheses h1, … ,hn
Given the following situation:
Hypothesis ENS = {e1,e2,e3,e4,e5} & e2 = e5 Goal e5 = e1
|
It is clear that the hypothesis e2 = e5 is contradictory. By applying the command:
PRI> fh(e2=e5) Starting False Hypothesis
|
the current goal becomes:
Goal not(e2 = e5)
|
by calling the automatic prover the goal can then be discharged.
PRI> pr Starting Prover Call
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