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Cslib/Languages/LambdaCalculus/Unscoped/Untyped Expand file tree Collapse file tree Original file line number Diff line number Diff line change @@ -50,12 +50,15 @@ namespace BetaStar
5050
5151public theorem refl (t : Term) : BetaStar t t :=
5252 Relation.ReflTransGen.refl
53+
5354public theorem head {a b c} (hab : Beta a b) (hbc : BetaStar b c) :
5455 BetaStar a c :=
5556 Relation.ReflTransGen.head hab hbc
57+
5658public theorem tail {a b c} (hab : BetaStar a b) (hbc : Beta b c) :
5759 BetaStar a c :=
5860 Relation.ReflTransGen.tail hab hbc
61+
5962public theorem trans {a b c}
6063 (hab : BetaStar a b) (hbc : BetaStar b c) :
6164 BetaStar a c :=
@@ -66,11 +69,13 @@ public theorem appL {t t' u : Term} (h : BetaStar t t') :
6669 induction h with
6770 | refl => exact BetaStar.refl (t·u)
6871 | tail hab hbc ih => exact BetaStar.tail ih (Beta.appL hbc)
72+
6973public theorem appR {t u u' : Term} (h : BetaStar u u') :
7074 BetaStar (t·u) (t·u') := by
7175 induction h with
7276 | refl => exact BetaStar.refl (t·u)
7377 | tail hab hbc ih => exact BetaStar.tail ih (Beta.appR hbc)
78+
7479public theorem app {t t' u u'}
7580 (ht : BetaStar t t')
7681 (hu : BetaStar u u') :
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