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Towards Intuitive Reasoning in Axiomatic Geometry
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.Comment: In Proceedings ThEdu'18, arXiv:1903.1240