Structural Proof Theory -

: Gentzen's most famous result, which states that any proof containing a "cut" (a detour or lemma) can be transformed into a cut-free (or normal) form.

The field is defined by two primary systems developed by in the 1930s: Structural Proof Theory

: Designed to mirror "natural" human reasoning by using rules for introducing and eliminating logical constants. : Gentzen's most famous result, which states that