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basic_2: stronger supclosure allows better inversion lemmas
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14
15 include "basic_2/notation/relations/pconv_4.ma".
16 include "basic_2/reduction/cpr.ma".
17
18 (* CONTEXT-SENSITIVE PARALLEL CONVERSION ON TERMS ***************************)
19
20 definition cpc: relation4 genv lenv term term ≝
21                 λG,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡ T2 ∨ ⦃G, L⦄ ⊢ T2 ➡ T1.
22
23 interpretation
24    "context-sensitive parallel conversion (term)"
25    'PConv G L T1 T2 = (cpc G L T1 T2).
26
27 (* Basic properties *********************************************************)
28
29 lemma cpc_refl: ∀G,L. reflexive … (cpc G L).
30 /2 width=1 by or_intror/ qed.
31
32 lemma cpc_sym: ∀G,L. symmetric … (cpc L G).
33 #G #L #T1 #T2 * /2 width=1 by or_introl, or_intror/
34 qed-.
35
36 (* Basic forward lemmas *****************************************************)
37
38 lemma cpc_fwd_cpr: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌ T2 → ∃∃T. ⦃G, L⦄ ⊢ T1 ➡ T & ⦃G, L⦄ ⊢ T2 ➡ T.
39 #G #L #T1 #T2 * /2 width=3 by ex2_intro/
40 qed-.