1. Conditional Proof
2. Examples
3. Nested Subproofs
4. Examples
6. Examples
5. Tautologies
Lecture 9
Conditional Proof,
Nested Subproofs, &
Tautologies
Second of two ‘proof strategies’
Conditional Proof
Basic idea: prove the conditional
!
㱭
!
is true, by assuming
!
and
deriving
!
.
At some point in a proof, you
decide you’d like to be able to
derive
!
㱭
!
on a line, but you
can’t figure out how. Add an
assumption line consisting of
!
,
then proceed using the rules.
Conditional Proof
Keep deriving lines until you
derive
!
. At this point, we don’t
know whether
!
is actually true,
since we just assumed it, but we
have shown that if
!
were true,
then
!
would be true.
Conditional Proof
But this fact that the subproof
demonstrated, that if
!
is true,
then
!
is true, just is what the
conditional
!
㱭
!
means. So the
subproof shows that the
conditional can be validly infered.
Conditional Proof
Rules for the use of CP
2.
CP ends any time you want
1. Start subproof (SP) by indenting
and designating first line ACP
3. Mark off CP, closing SP and
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 Spring '08
 churchland
 1920, 1922, 1916, 1913, 1918, 1925

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