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14
15 include "basic_2/substitution/drop.ma".
16 include "apps_2/models/model_li.ma".
17 include "apps_2/models/model_lift.ma".
18
19 (* MODEL ********************************************************************)
20
21 (* Properties on basic slicing **********************************************)
22
23 lemma sound_drop: ∀M. sound M → extensional M →
24                   ∀sv,gv,L,K,s,l,m. ⬇[s, l, m] L ≡ K →
25                   ∀lv. lv ∈ 〚L〛⦋M⦌{sv, gv} → ↓[l, m] lv ∈ 〚K〛⦋M⦌{sv, gv}.
26 #M #H1M #H2M #sv #gv #L #K #s #l #m #H elim H -l -m /2 width=3 by li_veq/
27 [ * #L #K #V #m #_ #IHLK #x #H -H1M -H2M
28   [ elim (li_inv_ldef … H) | elim (li_inv_ldec … H) ] -H
29   /4 width=5 by li_veq, lower_raise_be, lower_veq/ (* 2 x li_veq *)
30 | * #L #K #W #V #l #m #_ #HVW #IHLK #x #H
31   [ elim (li_inv_ldef … H) #lv | elim (li_inv_ldec … H) #lv #d ] -H
32   <(sound_fwd_lift M H1M H2M sv gv … HVW lv) -H1M -H2M -HVW
33   /5 width=6 by li_veq, li_ldec, li_ldef, lower_raise_lt, lower_veq/ (* 2 x li_veq *)
34 ]
35 qed-.