Standard abs inv
Cslib.LambdaCalculus.LocallyNameless.Untyped.Term.Standard.abs_inv
Plain-language statement
If a standard reduction reaches an abstraction, then its leading Call-by-Name reduction reaches an abstraction that standardly reduces to the same target.
Exact Lean statement
lemma Standard.abs_inv (h : M ⭢ₛ N) (M' : Term Var) (eq : N = Term.abs M') :
∃ M'', M ↠ₙ Term.abs M'' ∧ Term.abs M'' ⭢ₛ Term.abs M'Formal artifact
Lean source
lemma Standard.abs_inv (h : M ⭢ₛ N) (M' : Term Var) (eq : N = Term.abs M') : ∃ M'', M ↠ₙ Term.abs M'' ∧ Term.abs M'' ⭢ₛ Term.abs M' := by induction h generalizing M' case fvar => trivial case app => trivial case abs m_body m_target xs h_body ih => cases eq exact ⟨m_body, .refl, .abs xs h_body⟩ case rdx m1 n1 m1' p1 lc_m1 lc_n1 cbn_m1 _ ih => have ⟨p'', cbn_body, std_p''⟩ := ih M' eq have step1 : m1.app n1 ↠ₙ m1'.abs.app n1 := CBN.steps_app_l_cong cbn_m1 lc_n1 have step2 : m1'.abs.app n1 ⭢ₙ m1' ^ n1 := .base (.beta (CBN.steps_lc_r lc_m1 cbn_m1) lc_n1) exact ⟨p'', .trans step1 (.head step2 cbn_body), std_p''⟩- Project
- Lean Computer Science Library
- License
- Apache-2.0
- Commit
- f36649cff2c9
- Source
- Cslib/Languages/LambdaCalculus/LocallyNameless/Untyped/StandardReduction.lean:145-157
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Person-level attribution pending.
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