Sn app
Cslib.LambdaCalculus.LocallyNameless.Untyped.Term.sn_app
Plain-language statement
An application is strongly normalizing if the left and right terms are strongly normalizing, as well as all possible future top level abstraction application beta reductions
Exact Lean statement
lemma sn_app (t s : Term Var) (sn_t : SN FullBeta t) (sn_s : SN FullBeta s)
(hβ : ∀ {t' s' : Term Var}, t ↠βᶠ t'.abs → s ↠βᶠ s' → SN FullBeta (t' ^ s')) :
SN FullBeta (t.app s)Formal artifact
Lean source
lemma sn_app (t s : Term Var) (sn_t : SN FullBeta t) (sn_s : SN FullBeta s) (hβ : ∀ {t' s' : Term Var}, t ↠βᶠ t'.abs → s ↠βᶠ s' → SN FullBeta (t' ^ s')) : SN FullBeta (t.app s) := by induction sn_t generalizing s with | intro t ht ih_t => induction sn_s with | intro s hs ih_s => constructor intro u hstep cases hstep with | base h => cases h; grind | appL _ h_s_red => apply ih_s _ h_s_red grind [Relation.ReflTransGen.head] | appR _ h_t_red => apply ih_t _ h_t_red _ (SN.intro hs) grind [Relation.ReflTransGen.head]- Project
- Lean Computer Science Library
- License
- Apache-2.0
- Commit
- f36649cff2c9
- Source
- Cslib/Languages/LambdaCalculus/LocallyNameless/Untyped/StrongNorm.lean:48-62
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