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- extended multiple substitutions now uses bounds in ynat (ie. they
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14
15 include "basic_2/grammar/bteq.ma".
16
17 (* EQUIVALENT "BIG TREE" NORMAL FORMS ***************************************)
18
19 (* Main properties **********************************************************)
20
21 theorem bteq_trans: tri_transitive … bteq.
22 #G1 #G #L1 #L #T1 #T * //
23 qed-.
24
25 theorem bteq_canc_sn: ∀G,G1,G2,L,L1,L2,T,T1,T2. ⦃G, L, T⦄ ⋕ ⦃G1, L1, T1⦄ →
26                       ⦃G, L, T⦄ ⋕ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ⋕ ⦃G2, L2, T2⦄.
27 /3 width=5 by bteq_trans, bteq_sym/ qed-.
28
29 theorem bteq_canc_dx: ∀G1,G2,G,L1,L2,L,T1,T2,T. ⦃G1, L1, T1⦄ ⋕ ⦃G, L, T⦄ →
30                       ⦃G2, L2, T2⦄ ⋕ ⦃G, L, T⦄ → ⦃G1, L1, T1⦄ ⋕ ⦃G2, L2, T2⦄.
31 /3 width=5 by bteq_trans, bteq_sym/ qed-.