matita/matita/contribs/lambdadelta/basic_2/etc/cpcs/cpcs_cpcs.etc

   1 lemma cpcs_beta_dx: ∀a,L,V1,V2,W1,W2,T1,T2.
   2                     L ⊢ V1 ⬌* V2 → L ⊢ W1 ⬌* W2 → L.ⓛW2 ⊢ T1 ⬌* T2 →
   3                     L ⊢ ⓐV1.ⓛ{a}W1.T1 ⬌* ⓓ{a}ⓝW2.V2.T2.
   4 #a #L #V1 #V2 #W1 #W2 #T1 #T2 #HV12 #HW12 #HT12
   5 @(cpcs_cpr_strap1 … (ⓐV2.ⓛ{a}W2.T2)) /2 width=1/ /3 width=1/
   6 qed.
   7
   8 lemma cpcs_beta_sn: ∀a,L,V1,V2,W1,W2,T1,T2.
   9                     L ⊢ V1 ⬌* V2 → L ⊢ W1 ⬌* W2 → L.ⓛW1 ⊢ T1 ⬌* T2 →
  10                     L ⊢ ⓐV1.ⓛ{a}W1.T1 ⬌* ⓓ{a}ⓝW2.V2.T2.
  11 #a #L #V1 #V2 #W1 #W2 #T1 #T2 #HV12 #HW12 #HT12
  12 lapply (lsubr_cpcs_trans … HT12 (L.ⓓⓝW1.V1) ?) /2 width=1/ #H2T12
  13 @(cpcs_cpr_strap2 … (ⓓ{a}ⓝW1.V1.T1)) /2 width=1/ -HT12 /3 width=1/
  14 qed.