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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "ground/relocation/pr_tl_eq.ma".
17 (* TAIL FOR PARTIAL RELOCATION MAPS *****************************************)
19 (* Main constructions with pr_eq ********************************************)
22 corec theorem pr_eq_trans: Transitive … pr_eq.
24 #f1 #f #g1 #g #Hf1 #H1 #H #f2 #Hf2
25 [ cases (pr_eq_inv_push_sn … Hf2 … H)
26 | cases (pr_eq_inv_next_sn … Hf2 … H)
28 /3 width=5 by pr_eq_push, pr_eq_next/
32 theorem pr_eq_canc_sn (f2): pr_eq_repl_back (λf. f ≡ f2).
33 /3 width=3 by pr_eq_trans, pr_eq_sym/ qed-.
36 theorem pr_eq_canc_dx (f1): pr_eq_repl_fwd (λf. f1 ≡ f).
37 /3 width=5 by pr_eq_canc_sn, pr_eq_repl_sym/ qed-.