Editing Proof Theory (section)

== <span style="color: #FFFFFF;">Analyzing</span> ==
{| class="wikitable"
|+ Constructive vs. Non-Constructive Proofs
! Feature !! Non-Constructive (Classical) !! Constructive (Intuitionistic)
|-
| Logic || Uses 'Law of Excluded Middle' || Does not assume P or NOT P
|-
| Outcome || Shows 'Existence' || Provides an 'Algorithm'
|-
| Computer Use || Hard to convert to code || Directly converts to a program
|-
| Example || There must be an even number here || Here is the even number: 4
|}

'''The Concept of "Structural Rules"''': These are the hidden rules of logic, like "Contraction" (using an assumption twice) and "Weakening" (adding a useless assumption). Proof theorists analyze what happens to a system if you ''remove'' these rules. This leads to new types of logic used in quantum physics and computer security.
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