-fact lifts_fwd_vlift_aux (M) (gv): is_model M → is_extensional M →
- ∀f,T1,T2. ⬆*[f] T1 ≘ T2 → ∀m. 𝐁❴m,1❵ = f →
- ∀lv,d. ⟦T1⟧[gv, lv] ≗{M} ⟦T2⟧[gv, ⫯[m←d]lv].
-#M #gv #H1M #H2M #f #T1 #T2 #H elim H -f -T1 -T2
-[ /4 width=3 by seq_trans, seq_sym, ms/
-| #f #i1 #i2 #Hi12 #m #Hm #lv #d destruct
- @(mr … H1M) [4,5: @(seq_sym … H1M) @(ml … H1M) |1,2: skip ]
+fact lifts_fwd_vpush_aux (M): is_model M → is_extensional M →
+ ∀f,T1,T2. ⇧*[f] T1 ≘ T2 → ∀m. 𝐛❨m,1❩ = f →
+ ∀gv,lv,d. ⟦T1⟧[gv,lv] ≗{M} ⟦T2⟧[gv,⫯[m←d]lv].
+#M #H1M #H2M #f #T1 #T2 #H elim H -f -T1 -T2
+[ #f #s #m #Hf #gv #lv #d
+ @(mq … H1M) [4,5: /3 width=2 by seq_sym, ms/ |1,2: skip ]
+ /2 width=1 by mr/
+| #f #i1 #i2 #Hi12 #m #Hm #gv #lv #d destruct
+ @(mq … H1M) [4,5: /3 width=2 by seq_sym, ml/ |1,2: skip ]