ELFE is an interactive system for teaching basic proof methods in discrete mathematics. The user inputs a mathematical text written in fair English which is converted to a special data-structure of first-order formulas. Certain proof obligations implied by this intermediate representation are checked by automated theorem provers which try to either prove the obligations or find countermodels if an obligation is wrong. The result of the verification process is then returned to the user. ELFE is implemented in HASKELL and can be accessed via a reactive web interface or from the command line. Background libraries for sets, relations and functions have been developed. It has been tested by students in the beginning of their mathematical studies.

Proving lemmas in synthetic geometry is often a time-consuming endeavour since many intermediate lemmas need to be proven before interesting results can be obtained. Improvements in automated theorem provers (ATP) in recent years now mean they can prove many of these intermediate lemmas.The interactive theorem prover ELFE accepts mathematical texts written in fair English and verifies them with the help of ATP. Geometrical texts can thereby easily be formalized in ELFE, leaving only the cornerstones of a proof to be derived by the user. This allows for teaching axiomatic geometry to students without prior experience in formalized mathematics.

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