##  [Cut Elimination](/cut-elimination) 

  ##  [Cut Elimination](https://natural.quantumdictionary.io/cut-elimination-0) 

  

 [![Natural & Formal Sciences Dictionary](/sites/default/files/styles/large/public/2026-01/Natural%20%26%20Formal%20Sciences.png.webp?itok=2kCDRVQv)](/topic-specific-dictionaries/natural-formal-sciences)



**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A procedure in proof theory that transforms a sequent (or natural deduction) proof to remove cut inferences (applications of the 'cut' rule), producing a cut-free proof typically satisfying the subformula property.

 

 

 

 

 





 

 



 ##  [Cut Elimination](https://mathlogic.quantumdictionary.io/cut-elimination-1) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The proof transformation that removes cut inferences (applications of the cut rule) from a sequent-calculus style proof to produce a cut-free derivation of the same end-sequent, preserving provability while often changing proof structure and size.