-lemma cnv_cpms_trans (a) (h) (G) (L):
- ∀T1. ⦃G,L⦄ ⊢ T1 ![a,h] →
- ∀n,T2. ⦃G,L⦄ ⊢ T1 ➡*[n,h] T2 → ⦃G,L⦄ ⊢ T2 ![a,h].
+lemma cnv_cpm_trans (h) (a) (G) (L):
+ ∀T1. ❪G,L❫ ⊢ T1 ![h,a] →
+ ∀n,T2. ❪G,L❫ ⊢ T1 ➡[n,h] T2 → ❪G,L❫ ⊢ T2 ![h,a].
+/2 width=6 by cnv_cpm_trans_lpr/ qed-.
+
+(* Note: this is the preservation property *)
+lemma cnv_cpms_trans (h) (a) (G) (L):
+ ∀T1. ❪G,L❫ ⊢ T1 ![h,a] →
+ ∀n,T2. ❪G,L❫ ⊢ T1 ➡*[n,h] T2 → ❪G,L❫ ⊢ T2 ![h,a].