include "basic_2A/notation/relations/rdropstar_3.ma".
include "basic_2A/notation/relations/rdropstar_4.ma".
include "basic_2A/substitution/drop.ma".
include "basic_2A/notation/relations/rdropstar_3.ma".
include "basic_2A/notation/relations/rdropstar_4.ma".
include "basic_2A/substitution/drop.ma".
include "basic_2A/multiple/lifts_vector.ma".
(* ITERATED LOCAL ENVIRONMENT SLICING ***************************************)
include "basic_2A/multiple/lifts_vector.ma".
(* ITERATED LOCAL ENVIRONMENT SLICING ***************************************)
| drops_nil : ∀L. drops s (◊) L L
| drops_cons: ∀L1,L,L2,cs,l,m.
| drops_nil : ∀L. drops s (◊) L L
| drops_cons: ∀L1,L,L2,cs,l,m.
- drops s cs L1 L → ⬇[s, l, m] L ≡ L2 → drops s ({l, m} @ cs) L1 L2
+ drops s cs L1 L → ⬇[s, l, m] L ≡ L2 → drops s (❨l, m❩; cs) L1 L2
/2 width=4 by drops_inv_nil_aux/ qed-.
fact drops_inv_cons_aux: ∀L1,L2,s,cs. ⬇*[s, cs] L1 ≡ L2 →
/2 width=4 by drops_inv_nil_aux/ qed-.
fact drops_inv_cons_aux: ∀L1,L2,s,cs. ⬇*[s, cs] L1 ≡ L2 →
- ∀l,m,tl. cs = {l, m} @ tl →
+ ∀l,m,tl. cs = ❨l, m❩; tl →
∃∃L. ⬇*[s, tl] L1 ≡ L & ⬇[s, l, m] L ≡ L2.
#L1 #L2 #s #cs * -L1 -L2 -cs
[ #L #l #m #tl #H destruct
∃∃L. ⬇*[s, tl] L1 ≡ L & ⬇[s, l, m] L ≡ L2.
#L1 #L2 #s #cs * -L1 -L2 -cs
[ #L #l #m #tl #H destruct
-lemma drops_inv_cons: ∀L1,L2,s,l,m,cs. ⬇*[s, {l, m} @ cs] L1 ≡ L2 →
+lemma drops_inv_cons: ∀L1,L2,s,l,m,cs. ⬇*[s, ❨l, m❩; cs] L1 ≡ L2 →
∃∃L. ⬇*[s, cs] L1 ≡ L & ⬇[s, l, m] L ≡ L2.
/2 width=3 by drops_inv_cons_aux/ qed-.
∃∃L. ⬇*[s, cs] L1 ≡ L & ⬇[s, l, m] L ≡ L2.
/2 width=3 by drops_inv_cons_aux/ qed-.
-lemma drops_inv_skip2: â\88\80I,s,cs,cs2,i. cs â\96 i â\89¡ cs2 →
+lemma drops_inv_skip2: â\88\80I,s,cs,cs2,i. cs â\96 i â\89\98 cs2 →
∀L1,K2,V2. ⬇*[s, cs2] L1 ≡ K2. ⓑ{I} V2 →
∀L1,K2,V2. ⬇*[s, cs2] L1 ≡ K2. ⓑ{I} V2 →