-theorem drops_conf: ∀L1,L,s1,t1. ⬇*[s1, t1] L1 ≡ L →
- ∀L2,s2,t. ⬇*[s2, t] L1 ≡ L2 →
- ∀t2. t1 ⊚ t2 ≡ t → ⬇*[s2, t2] L ≡ L2.
-#L1 #L #s1 #t1 #H elim H -L1 -L -t1
-[ #t1 #_ #L2 #s2 #t #H #t2 #Ht12 elim (drops_inv_atom1 … H) -s1 -H
- #H #Ht destruct @drops_atom
- #H elim (after_inv_isid3 … Ht12) -Ht12 /2 width=1 by/
-| #I #K1 #K #V1 #t1 #_ #IH #L2 #s2 #t #H12 #t2 #Ht elim (after_inv_false1 … Ht) -Ht
- #u #H #Hu destruct /3 width=3 by drops_inv_drop1/
-| #I #K1 #K #V1 #V #t1 #_ #HV1 #IH #L2 #s2 #t #H #t2 #Ht elim (after_inv_true1 … Ht) -Ht
- #u2 #u * #H1 #H2 #Hu destruct
- [ elim (drops_inv_skip1 … H) -H /3 width=6 by drops_skip, lifts_div/
+theorem drops_conf: ∀L1,L,c1,f1. ⬇*[c1, f1] L1 ≡ L →
+ ∀L2,c2,f. ⬇*[c2, f] L1 ≡ L2 →
+ ∀f2. f1 ⊚ f2 ≡ f → ⬇*[c2, f2] L ≡ L2.
+#L1 #L #c1 #f1 #H elim H -L1 -L -f1
+[ #f1 #_ #L2 #c2 #f #HL2 #f2 #Hf12 elim (drops_inv_atom1 … HL2) -c1 -HL2
+ #H #Hf destruct @drops_atom
+ #H elim (after_inv_isid3 … Hf12) -Hf12 /2 width=1 by/
+| #I #K1 #K #V1 #f1 #_ #IH #L2 #c2 #f #HL2 #f2 #Hf elim (after_inv_Sxx … Hf) -Hf
+ #g #Hg #H destruct /3 width=3 by drops_inv_drop1/
+| #I #K1 #K #V1 #V #f1 #_ #HV1 #IH #L2 #c2 #f #HL2 #f2 #Hf elim (after_inv_Oxx … Hf) -Hf *
+ #g2 #g #Hf #H1 #H2 destruct
+ [ elim (drops_inv_skip1 … HL2) -HL2 /3 width=6 by drops_skip, lifts_div/