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14
15 include "basic_2/grammar/tstc.ma".
16
17 (* SAME TOP TERM CONSTRUCTOR ************************************************)
18
19 (* Main properties **********************************************************)
20
21 (* Basic_1: was: iso_trans *)
22 theorem tstc_trans: ∀T1,T. T1 ≃ T → ∀T2. T ≃ T2 → T1 ≃ T2.
23 #T1 #T * -T1 -T //
24 #I #V1 #V #T1 #T #X #H
25 elim (tstc_inv_pair1 … H) -H #V2 #T2 #H destruct //
26 qed.
27
28 theorem tstc_canc_sn: ∀T,T1. T ≃ T1 → ∀T2. T ≃ T2 → T1 ≃ T2.
29 /3 width=3/ qed.
30
31 theorem tstc_canc_dx: ∀T1,T. T1 ≃ T → ∀T2. T2 ≃ T → T1 ≃ T2.
32 /3 width=3/ qed.