lapply (cpms_trans … HT1 … HT2) -T <commutative_plus #HT12
/2 width=1 by cpms_inv_plus/
qed-.
-
-(* More advanced inversion lemmas *******************************************)
-(*
-lemma cpms_inv_appl_sn_decompose (h) (n) (G) (L) (V1) (T1):
- ∀X2. ⦃G,L⦄ ⊢ ⓐV1.T1 ➡*[n,h] X2 →
- ∃∃T2. ⦃G,L⦄ ⊢ T1 ➡*[n,h] T2 & ⦃G,L⦄ ⊢ ⓐV1.T2 ➡*[h] X2.
-#h #n #G #L #V1 #T1 #X2 #H
-@(cpms_ind_dx … H) -n -X2
-[ /2 width=3 by ex2_intro/
-| #n1 #n2 #X #X2 #_ * #X1 #HTX1 #HX1 #HX2
- elim (pippo … HX1 … HX2) -X #X #HX1 #HX2
- elim (cpm_inv_appl_sn_decompose … HX1) -HX1 #U1 #HXU1 #HU1X
- /3 width=5 by cprs_step_sn, cpms_step_dx, ex2_intro/
-]
-qed-.
-*)