matita/matita/contribs/lambdadelta/ground/relocation/pr_coafter_coafter.ma

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  14
  15 include "ground/relocation/pr_coafter_eq.ma".
  16
  17 (* RELATIONAL CO-COMPOSITION FOR PARTIAL RELOCATION MAPS ********************)
  18
  19 (* Main inversions **********************************************************)
  20
  21 (*** coafter_mono *)
  22 corec theorem pr_coafter_mono:
  23               ∀f1,f2,x,y. f1 ~⊚ f2 ≘ x → f1 ~⊚ f2 ≘ y → x ≡ y.
  24 #f1 #f2 #x #y * -f1 -f2 -x
  25 #f1 #f2 #x #g1 [1,2: #g2 ] #g #Hx #H1 [1,2: #H2 ] #H0x #Hy
  26 [ cases (pr_coafter_inv_push_bi … Hy … H1 H2) -g1 -g2 /3 width=8 by pr_eq_push/
  27 | cases (pr_coafter_inv_push_next … Hy … H1 H2) -g1 -g2 /3 width=8 by pr_eq_next/
  28 | cases (pr_coafter_inv_next_sn … Hy … H1) -g1 /3 width=8 by pr_eq_push/
  29 ]
  30 qed-.
  31
  32 (*** coafter_mono_eq *)
  33 lemma pr_coafter_mono_eq:
  34       ∀f1,f2,f. f1 ~⊚ f2 ≘ f → ∀g1,g2,g. g1 ~⊚ g2 ≘ g →
  35       f1 ≡ g1 → f2 ≡ g2 → f ≡ g.
  36 /4 width=4 by pr_coafter_mono, pr_coafter_eq_repl_back_dx, pr_coafter_eq_repl_back_sn/ qed-.