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15 include "ground/notation/relations/ideq_2.ma".
16 include "static_2/syntax/teqg.ma".
18 (* SYNTACTIC EQUIVALENCE ON TERMS *******************************************)
20 definition teq: relation term ≝
24 "context-free syntactic equivalence (term)"
25 'IdEq T1 T2 = (teq T1 T2).
27 (* Basic properties *********************************************************)
31 /2 width=1 by teqg_refl/ qed.
35 /2 width=1 by teqg_sym/ qed-.
37 (* Basic inversion lemmas ***************************************************)
40 ∀T1,T2. T1 ≡ T2 → T1 = T2.
41 #T1 #T2 #H elim H -H //
44 (* Advanced forward lemmas **************************************************)
46 lemma teq_repl_1 (R:predicate …):
47 ∀T1. R T1 → ∀T2. T1 ≡ T2 → R T2.
49 <(teq_inv_eq … HT12) -T2 //
52 lemma teq_sym_repl_1 (R:predicate …):
53 ∀T1. R T1 → ∀T2. T2 ≡ T1 → R T2.
55 >(teq_inv_eq … HT12) -T2 //