(* Basic forward lemmas *****************************************************)
lemma cpys_fwd_up: ∀G,L,U1,U2,dt,et. ⦃G, L⦄ ⊢ U1 ▶*[dt, et] U2 →
- â\88\80T1,d,e. â\87§[d, e] T1 ≡ U1 →
+ â\88\80T1,d,e. â¬\86[d, e] T1 ≡ U1 →
d ≤ dt → d + e ≤ dt + et →
- â\88\83â\88\83T2. â¦\83G, Lâ¦\84 â\8a¢ U1 â\96¶*[d+e, dt+et-(d+e)] U2 & â\87§[d, e] T2 ≡ U2.
+ â\88\83â\88\83T2. â¦\83G, Lâ¦\84 â\8a¢ U1 â\96¶*[d+e, dt+et-(d+e)] U2 & â¬\86[d, e] T2 ≡ U2.
#G #L #U1 #U2 #dt #et #H #T1 #d #e #HTU1 #Hddt #Hdedet @(cpys_ind … H) -U2
[ /2 width=3 by ex2_intro/
| -HTU1 #U #U2 #_ #HU2 * #T #HU1 #HTU
qed-.
lemma cpys_inv_lift1_eq: ∀G,L,U1,U2. ∀d,e:nat.
- â¦\83G, Lâ¦\84 â\8a¢ U1 â\96¶*[d, e] U2 â\86\92 â\88\80T1. â\87§[d, e] T1 ≡ U1 → U1 = U2.
+ â¦\83G, Lâ¦\84 â\8a¢ U1 â\96¶*[d, e] U2 â\86\92 â\88\80T1. â¬\86[d, e] T1 ≡ U1 → U1 = U2.
#G #L #U1 #U2 #d #e #H #T1 #HTU1 @(cpys_ind … H) -U2
/2 width=7 by cpy_inv_lift1_eq/
qed-.