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

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  14
  15 include "ground/relocation/gr_isf_eq.ma".
  16 include "ground/relocation/gr_sor_fcla.ma".
  17
  18 (* RELATIONAL UNION FOR GENERIC RELOCATION MAPS *****************************)
  19
  20 (* Constructions with gr_isf ************************************************)
  21
  22 (*** sor_isfin_ex *)
  23 lemma gr_sor_isf_bi:
  24       ∀f1,f2. 𝐅❪f1❫ → 𝐅❪f2❫ → ∃∃f. f1 ⋓ f2 ≘ f & 𝐅❪f❫.
  25 #f1 #f2 * #n1 #H1 * #n2 #H2 elim (gr_sor_fcla_bi … H1 … H2) -H1 -H2
  26 /3 width=4 by ex2_intro, ex_intro/
  27 qed-.
  28
  29 (* Destructions with gr_isf *************************************************)
  30
  31 (*** sor_fwd_isfin_sn *)
  32 lemma gr_sor_des_isf_sn:
  33       ∀f. 𝐅❪f❫ → ∀f1,f2. f1 ⋓ f2 ≘ f → 𝐅❪f1❫.
  34 #f * #n #Hf #f1 #f2 #H
  35 elim (gr_sor_des_fcla_sn … Hf … H) -f -f2 /2 width=2 by ex_intro/
  36 qed-.
  37
  38 (*** sor_fwd_isfin_dx *)
  39 lemma gr_sor_des_isf_dx:
  40       ∀f. 𝐅❪f❫ → ∀f1,f2. f1 ⋓ f2 ≘ f → 𝐅❪f2❫.
  41 #f * #n #Hf #f1 #f2 #H
  42 elim (gr_sor_des_fcla_dx … Hf … H) -f -f1 /2 width=2 by ex_intro/
  43 qed-.
  44
  45 (* Inversions with gr_isf ***************************************************)
  46
  47 (*** sor_isfin *)
  48 lemma gr_sor_inv_isf_bi:
  49       ∀f1,f2. 𝐅❪f1❫ → 𝐅❪f2❫ → ∀f. f1 ⋓ f2 ≘ f → 𝐅❪f❫.
  50 #f1 #f2 #Hf1 #Hf2 #f #Hf elim (gr_sor_isf_bi … Hf1 … Hf2) -Hf1 -Hf2
  51 /3 width=6 by gr_sor_mono, gr_isf_eq_repl_back/
  52 qed-.
  53
  54 (*** sor_inv_isfin3 *)
  55 lemma gr_sor_inv_isf:
  56       ∀f1,f2,f. f1 ⋓ f2 ≘ f → 𝐅❪f❫ →
  57       ∧∧ 𝐅❪f1❫ & 𝐅❪f2❫.
  58 /3 width=4 by gr_sor_des_isf_dx, gr_sor_des_isf_sn, conj/ qed-.