(* Properties with t-unbound whd evaluation on terms ************************)
-lemma cnv_cpmuwe_trans (a) (h) (G) (L):
- â\88\80T1. â¦\83G,Lâ¦\84 â\8a¢ T1 ![a,h] →
- ∀T2,n. ⦃G,L⦄ ⊢ T1 ➡*𝐍𝐖*[h,n] T2 → ⦃G,L⦄ ⊢ T2 ![a,h].
+lemma cnv_cpmuwe_trans (h) (a) (G) (L):
+ â\88\80T1. â\9dªG,Lâ\9d« â\8a¢ T1 ![h,a] →
+ ∀n,T2. ❪G,L❫ ⊢ T1 ➡*𝐍𝐖*[h,n] T2 → ❪G,L❫ ⊢ T2 ![h,a].
/3 width=4 by cpmuwe_fwd_cpms, cnv_cpms_trans/ qed-.
-lemma cnv_R_cpmuwe_total (a) (h) (G) (L):
- â\88\80T1. â¦\83G,Lâ¦\84 â\8a¢ T1 ![a,h] → ∃n. R_cpmuwe h G L T1 n.
-/4 width=2 by cnv_fwd_fsb, fsb_inv_csx, R_cpmuwe_total_csx/ qed-.
+lemma cnv_R_cpmuwe_total (h) (a) (G) (L):
+ â\88\80T1. â\9dªG,Lâ\9d« â\8a¢ T1 ![h,a] → ∃n. R_cpmuwe h G L T1 n.
+/4 width=3 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 (a) (h) (G) (L):
- ∀T0. ⦃G,L⦄ ⊢ T0 ![a,h] → ∀T1,n1. ⦃G,L⦄ ⊢ T0 ➡*𝐍𝐖*[h,n1] T1 →
- ∀T2,n2. ⦃G,L⦄ ⊢ T0 ➡*𝐍𝐖*[h,n2] T2 →
- ∧∧ ⦃G,L⦄ ⊢ T1 ⬌*[h,n2-n1,n1-n2] T2 & T1 ≅ T2.
-#a #h #G #L #T0 #HT0 #T1 #n1 * #HT01 #HT1 #T2 #n2 * #HT02 #HT2
+theorem cnv_cpmuwe_mono (h) (a) (G) (L):
+ ∀T0. ❪G,L❫ ⊢ T0 ![h,a] →
+ ∀n1,T1. ❪G,L❫ ⊢ T0 ➡*𝐍𝐖*[h,n1] T1 →
+ ∀n2,T2. ❪G,L❫ ⊢ T0 ➡*𝐍𝐖*[h,n2] T2 →
+ ∧∧ ❪G,L❫ ⊢ 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/
+/4 width=4 by cpms_div, teqw_canc_dx, conj/
qed-.