matita/matita/contribs/lambdadelta/basic_2A/multiple/fleq_fleq.ma

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  14
  15 include "basic_2A/multiple/lleq_lleq.ma".
  16 include "basic_2A/multiple/fleq.ma".
  17
  18 (* LAZY EQUIVALENCE FOR CLOSURES  *******************************************)
  19
  20 (* Main properties **********************************************************)
  21
  22 theorem fleq_trans: ∀l. tri_transitive … (fleq l).
  23 #l #G1 #G #L1 #L #T1 #T * -G -L -T
  24 #L #HT1 #G2 #L2 #T2 * -G2 -L2 -T2
  25 /3 width=3 by lleq_trans, fleq_intro/
  26 qed-.
  27
  28 theorem fleq_canc_sn: ∀G,G1,G2,L,L1,L2,T,T1,T2,l.
  29                       ⦃G, L, T⦄ ≡[l] ⦃G1, L1, T1⦄→ ⦃G, L, T⦄ ≡[l] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≡[l] ⦃G2, L2, T2⦄.
  30 /3 width=5 by fleq_trans, fleq_sym/ qed-.
  31
  32 theorem fleq_canc_dx: ∀G1,G2,G,L1,L2,L,T1,T2,T,l.
  33                       ⦃G1, L1, T1⦄ ≡[l] ⦃G, L, T⦄ → ⦃G2, L2, T2⦄ ≡[l] ⦃G, L, T⦄ → ⦃G1, L1, T1⦄ ≡[l] ⦃G2, L2, T2⦄.
  34 /3 width=5 by fleq_trans, fleq_sym/ qed-.