definition IH_cnv_cpm_teqx_cpm_trans (h) (a): relation3 genv lenv term ≝
λG,L,T1. ❪G,L❫ ⊢ T1 ![h,a] →
- ∀n1,T. ❪G,L❫ ⊢ T1 ➡[n1,h] T → T1 ≛ T →
- ∀n2,T2. ❪G,L❫ ⊢ T ➡[n2,h] T2 →
- ∃∃T0. ❪G,L❫ ⊢ T1 ➡[n2,h] T0 & ❪G,L❫ ⊢ T0 ➡[n1,h] T2 & T0 ≛ T2.
+ ∀n1,T. ❪G,L❫ ⊢ T1 ➡[h,n1] T → T1 ≛ T →
+ ∀n2,T2. ❪G,L❫ ⊢ T ➡[h,n2] T2 →
+ ∃∃T0. ❪G,L❫ ⊢ T1 ➡[h,n2] T0 & ❪G,L❫ ⊢ T0 ➡[h,n1] T2 & T0 ≛ T2.
(* Transitive properties restricted rt-transition for terms *****************)