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lines changed Original file line number Diff line number Diff line change @@ -409,8 +409,7 @@ performing enough beta reductions in parallel.
409409
410410However, a simpler approach is to perform as many beta reductions in
411411parallel as possible on ` M ` , say ` M ⁺ ` , and then show that ` N ` also
412- parallel reduces to ` M ⁺ ` . This is the idea of Takahashi's _ complete
413- development_ . The desired property may be illustrated as
412+ parallel reduces to ` M ⁺ ` . The desired property may be illustrated as
414413
415414 M
416415 /|
@@ -607,13 +606,9 @@ confluence L↠M₁ L↠M₂
607606
608607## Notes
609608
610- This mechanized proof of confluence is based on several sources. The
611- ` subst-par ` lemma is the "strong substitutivity" lemma of
612- @Schafer :2015. The proofs of ` par-triangle ` , ` strip ` ,
613- and ` par-confluence ` are based on the notion of complete development
614- by @Takahashi :1995 and the technical report by @Pfenning :1992 about the
615- Church-Rosser theorem. In addition, we consulted Nipkow and
616- Berghofer's mechanization in Isabelle, which is based on an earlier
609+ This mechanized proof of confluence is loosely based on several
610+ sources including @Schafer :2015, @Takahashi :1995, @Pfenning :1992, and
611+ Nipkow and Berghofer's mechanization in Isabelle, which is based on a
617612paper by @Nipkow :1996.
618613
619614## Unicode
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