つづき

他の証明手法との関係
Refutation by contradiction
Proof by contradiction is similar to refutation by contradiction,[30][31] also known as proof of negation, which states that ¬P is proved as follows:
1.The proposition to be proved is ¬P.
2.Assume P.
3.Derive falsehood.
4.Conclude ¬P.

In contrast, proof by contradiction proceeds as follows:
1.The proposition to be proved is P.
2.Assume ¬P.
3.Derive falsehood.
4.Conclude P.
Formally these are not the same, as refutation by contradiction applies only when the proposition to be proved is negated, whereas proof by contradiction may be applied to any proposition whatsoever.[32] In classical logic, where
P and ¬¬P may be freely interchanged, the distinction is largely obscured. Thus in mathematical practice, both principles are referred to as "proof by contradiction".

Proof by contradiction in intuitionistic logic
In intuitionistic logic proof by contradiction is not generally valid, although some particular instances can be derived. In contrast, proof of negation and principle of noncontradiction are both intuitionistically valid.[33]
(引用終り)
以上