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

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  14
  15 include "ground/relocation/pr_nat.ma".
  16 include "ground/relocation/pr_after_pat.ma".
  17
  18 (* RELATIONAL COMPOSITION FOR PARTIAL RELOCATION MAPS ***********************)
  19
  20 (* Destructions with pr_nat *************************************************)
  21
  22 lemma pr_after_nat_des (l) (l1):
  23       ∀f. ＠§❨l1, f❩ ≘ l → ∀f2,f1. f2 ⊚ f1 ≘ f →
  24       ∃∃l2. ＠§❨l1, f1❩ ≘ l2 & ＠§❨l2, f2❩ ≘ l.
  25 #l #l1 #f #H1 #f2 #f1 #Hf
  26 elim (pr_after_pat_des … H1 … Hf) -f #i2 #H1 #H2
  27 /2 width=3 by ex2_intro/
  28 qed-.
  29
  30 lemma pr_after_des_nat (l) (l2) (l1):
  31       ∀f1,f2. ＠§❨l1, f1❩ ≘ l2 → ＠§❨l2, f2❩ ≘ l →
  32       ∀f. f2 ⊚ f1 ≘ f → ＠§❨l1, f❩ ≘ l.
  33 /2 width=6 by pr_after_des_pat/ qed-.
  34
  35 lemma pr_after_des_nat_sn (l1) (l):
  36       ∀f. ＠§❨l1, f❩ ≘ l → ∀f1,l2. ＠§❨l1, f1❩ ≘ l2 →
  37       ∀f2. f2 ⊚ f1 ≘ f → ＠§❨l2, f2❩ ≘ l.
  38 /2 width=6 by pr_after_des_pat_sn/ qed-.
  39
  40 lemma pr_after_des_nat_dx (l) (l2) (l1):
  41       ∀f,f2. ＠§❨l1, f❩ ≘ l → ＠§❨l2, f2❩ ≘ l →
  42       ∀f1. f2 ⊚ f1 ≘ f → ＠§❨l1, f1❩ ≘ l2.
  43 /2 width=6 by pr_after_des_pat_dx/ qed-.