(* Properties with t-unbound whd evaluation on terms ************************)
lemma cnv_cpmuwe_trans (h) (a) (G) (L):
- â\88\80T1. â¦\83G,Lâ¦\84 ⊢ T1 ![h,a] →
- â\88\80n,T2. â¦\83G,Lâ¦\84 â\8a¢ T1 â\9e¡*ð\9d\90\8dð\9d\90\96*[h,n] T2 â\86\92 â¦\83G,Lâ¦\84 ⊢ T2 ![h,a].
+ â\88\80T1. â\9dªG,Lâ\9d« ⊢ T1 ![h,a] →
+ â\88\80n,T2. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡*ð\9d\90\8dð\9d\90\96*[h,n] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ T2 ![h,a].
/3 width=4 by cpmuwe_fwd_cpms, cnv_cpms_trans/ qed-.
lemma cnv_R_cpmuwe_total (h) (a) (G) (L):
- â\88\80T1. â¦\83G,Lâ¦\84 ⊢ T1 ![h,a] → ∃n. R_cpmuwe h G L T1 n.
+ â\88\80T1. â\9dªG,Lâ\9d« ⊢ T1 ![h,a] → ∃n. R_cpmuwe h G L T1 n.
/4 width=2 by cnv_fwd_fsb, fsb_inv_csx, R_cpmuwe_total_csx/ qed-.
(* Main inversions with head evaluation for t-bound rt-transition on terms **)
theorem cnv_cpmuwe_mono (h) (a) (G) (L):
- â\88\80T0. â¦\83G,Lâ¦\84 ⊢ T0 ![h,a] →
- â\88\80n1,T1. â¦\83G,Lâ¦\84 ⊢ T0 ➡*𝐍𝐖*[h,n1] T1 →
- â\88\80n2,T2. â¦\83G,Lâ¦\84 ⊢ T0 ➡*𝐍𝐖*[h,n2] T2 →
- â\88§â\88§ â¦\83G,Lâ¦\84 ⊢ T1 ⬌*[h,n2-n1,n1-n2] T2 & T1 ≅ T2.
+ â\88\80T0. â\9dªG,Lâ\9d« ⊢ T0 ![h,a] →
+ â\88\80n1,T1. â\9dªG,Lâ\9d« ⊢ T0 ➡*𝐍𝐖*[h,n1] T1 →
+ â\88\80n2,T2. â\9dªG,Lâ\9d« ⊢ T0 ➡*𝐍𝐖*[h,n2] T2 →
+ â\88§â\88§ â\9dªG,Lâ\9d« ⊢ T1 ⬌*[h,n2-n1,n1-n2] T2 & T1 ≅ T2.
#h #a #G #L #T0 #HT0 #n1 #T1 * #HT01 #HT1 #n2 #T2 * #HT02 #HT2
elim (cnv_cpms_conf … HT0 … HT01 … HT02) -T0 #T0 #HT10 #HT20
/4 width=4 by cpms_div, tweq_canc_dx, conj/