update in ground_2, static_2, basic_2, apps_2, alpha_1

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / static / rex.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/rex.ma b/matita/matita/contribs/lambdadelta/static_2/static/rex.ma
index bfaf0cbce5d2b0cb831b246a216a7097384b359c..a17dd7d6a469800699feca0ad9324210d0150adf 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/rex.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/rex.ma
@@ -25,7 +25,7 @@ include "static_2/static/frees.ma".
 (* GENERIC EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ****)
 
 definition rex (R) (T): relation lenv ≝
-               λL1,L2. â\88\83â\88\83f. L1 â\8a¢ ð\9d\90\85+â¦\83Tâ¦\84 ≘ f & L1 ⪤[cext2 R,cfull,f] L2.
+               λL1,L2. â\88\83â\88\83f. L1 â\8a¢ ð\9d\90\85+â\9dªTâ\9d« ≘ f & L1 ⪤[cext2 R,cfull,f] L2.
 
 interpretation "generic extension on referred entries (local environment)"
    'Relation R T L1 L2 = (rex R T L1 L2).
@@ -60,7 +60,7 @@ qed-.
 lemma rex_inv_sort (R):
       ∀Y1,Y2,s. Y1 ⪤[R,⋆s] Y2 →
       ∨∨ ∧∧ Y1 = ⋆ & Y2 = ⋆
-       | ∃∃I1,I2,L1,L2. L1 ⪤[R,⋆s] L2 & Y1 = L1.ⓘ{I1} & Y2 = L2.ⓘ{I2}.
+       | ∃∃I1,I2,L1,L2. L1 ⪤[R,⋆s] L2 & Y1 = L1.ⓘ[I1] & Y2 = L2.ⓘ[I2].
 #R * [ | #Y1 #I1 ] #Y2 #s * #f #H1 #H2
 [ lapply (sex_inv_atom1 … H2) -H2 /3 width=1 by or_introl, conj/
 | lapply (frees_inv_sort … H1) -H1 #Hf
@@ -74,9 +74,9 @@ lemma rex_inv_zero (R):
       ∀Y1,Y2. Y1 ⪤[R,#0] Y2 →
       ∨∨ Y1 = ⋆ ∧ Y2 = ⋆
        | ∃∃I,L1,L2,V1,V2. L1 ⪤[R,V1] L2 & R L1 V1 V2 &
-           Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2
-       | â\88\83â\88\83f,I,L1,L2. ð\9d\90\88â¦\83fâ¦\84 & L1 ⪤[cext2 R,cfull,f] L2 &
-           Y1 = L1.ⓤ{I} & Y2 = L2.ⓤ{I}.
+           Y1 = L1.ⓑ[I]V1 & Y2 = L2.ⓑ[I]V2
+       | â\88\83â\88\83f,I,L1,L2. ð\9d\90\88â\9dªfâ\9d« & L1 ⪤[cext2 R,cfull,f] L2 &
+           Y1 = L1.ⓤ[I] & Y2 = L2.ⓤ[I].
 #R * [ | #Y1 * #I1 [ | #X ] ] #Y2 * #f #H1 #H2
 [ lapply (sex_inv_atom1 … H2) -H2 /3 width=1 by or3_intro0, conj/
 | elim (frees_inv_unit … H1) -H1 #g #HX #H destruct
@@ -92,7 +92,7 @@ qed-.
 lemma rex_inv_lref (R):
       ∀Y1,Y2,i. Y1 ⪤[R,#↑i] Y2 →
       ∨∨ ∧∧ Y1 = ⋆ & Y2 = ⋆
-       | ∃∃I1,I2,L1,L2. L1 ⪤[R,#i] L2 & Y1 = L1.ⓘ{I1} & Y2 = L2.ⓘ{I2}.
+       | ∃∃I1,I2,L1,L2. L1 ⪤[R,#i] L2 & Y1 = L1.ⓘ[I1] & Y2 = L2.ⓘ[I2].
 #R * [ | #Y1 #I1 ] #Y2 #i * #f #H1 #H2
 [ lapply (sex_inv_atom1 … H2) -H2 /3 width=1 by or_introl, conj/
 | elim (frees_inv_lref … H1) -H1 #g #Hg #H destruct
@@ -104,7 +104,7 @@ qed-.
 lemma rex_inv_gref (R):
       ∀Y1,Y2,l. Y1 ⪤[R,§l] Y2 →
       ∨∨ ∧∧ Y1 = ⋆ & Y2 = ⋆
-       | ∃∃I1,I2,L1,L2. L1 ⪤[R,§l] L2 & Y1 = L1.ⓘ{I1} & Y2 = L2.ⓘ{I2}.
+       | ∃∃I1,I2,L1,L2. L1 ⪤[R,§l] L2 & Y1 = L1.ⓘ[I1] & Y2 = L2.ⓘ[I2].
 #R * [ | #Y1 #I1 ] #Y2 #l * #f #H1 #H2
 [ lapply (sex_inv_atom1 … H2) -H2 /3 width=1 by or_introl, conj/
 | lapply (frees_inv_gref … H1) -H1 #Hf
@@ -116,15 +116,15 @@ qed-.
 
 (* Basic_2A1: uses: llpx_sn_inv_bind llpx_sn_inv_bind_O *)
 lemma rex_inv_bind (R):
-      ∀p,I,L1,L2,V1,V2,T. L1 ⪤[R,ⓑ{p,I}V1.T] L2 → R L1 V1 V2 →
-      ∧∧ L1 ⪤[R,V1] L2 & L1.ⓑ{I}V1 ⪤[R,T] L2.ⓑ{I}V2.
+      ∀p,I,L1,L2,V1,V2,T. L1 ⪤[R,ⓑ[p,I]V1.T] L2 → R L1 V1 V2 →
+      ∧∧ L1 ⪤[R,V1] L2 & L1.ⓑ[I]V1 ⪤[R,T] L2.ⓑ[I]V2.
 #R #p #I #L1 #L2 #V1 #V2 #T * #f #Hf #HL #HV elim (frees_inv_bind … Hf) -Hf
 /6 width=6 by sle_sex_trans, sex_inv_tl, ext2_pair, sor_inv_sle_dx, sor_inv_sle_sn, ex2_intro, conj/
 qed-.
 
 (* Basic_2A1: uses: llpx_sn_inv_flat *)
 lemma rex_inv_flat (R):
-      ∀I,L1,L2,V,T. L1 ⪤[R,ⓕ{I}V.T] L2 →
+      ∀I,L1,L2,V,T. L1 ⪤[R,ⓕ[I]V.T] L2 →
       ∧∧ L1 ⪤[R,V] L2 & L1 ⪤[R,T] L2.
 #R #I #L1 #L2 #V #T * #f #Hf #HL elim (frees_inv_flat … Hf) -Hf
 /5 width=6 by sle_sex_trans, sor_inv_sle_dx, sor_inv_sle_sn, ex2_intro, conj/
@@ -133,8 +133,8 @@ qed-.
 (* Advanced inversion lemmas ************************************************)
 
 lemma rex_inv_sort_bind_sn (R):
-      ∀I1,K1,L2,s. K1.ⓘ{I1} ⪤[R,⋆s] L2 →
-      ∃∃I2,K2. K1 ⪤[R,⋆s] K2 & L2 = K2.ⓘ{I2}.
+      ∀I1,K1,L2,s. K1.ⓘ[I1] ⪤[R,⋆s] L2 →
+      ∃∃I2,K2. K1 ⪤[R,⋆s] K2 & L2 = K2.ⓘ[I2].
 #R #I1 #K1 #L2 #s #H elim (rex_inv_sort … H) -H *
 [ #H destruct
 | #Z1 #I2 #Y1 #K2 #Hs #H1 #H2 destruct /2 width=4 by ex2_2_intro/
@@ -142,8 +142,8 @@ lemma rex_inv_sort_bind_sn (R):
 qed-.
 
 lemma rex_inv_sort_bind_dx (R):
-      ∀I2,K2,L1,s. L1 ⪤[R,⋆s] K2.ⓘ{I2} →
-      ∃∃I1,K1. K1 ⪤[R,⋆s] K2 & L1 = K1.ⓘ{I1}.
+      ∀I2,K2,L1,s. L1 ⪤[R,⋆s] K2.ⓘ[I2] →
+      ∃∃I1,K1. K1 ⪤[R,⋆s] K2 & L1 = K1.ⓘ[I1].
 #R #I2 #K2 #L1 #s #H elim (rex_inv_sort … H) -H *
 [ #_ #H destruct
 | #I1 #Z2 #K1 #Y2 #Hs #H1 #H2 destruct /2 width=4 by ex2_2_intro/
@@ -151,8 +151,8 @@ lemma rex_inv_sort_bind_dx (R):
 qed-.
 
 lemma rex_inv_zero_pair_sn (R):
-      ∀I,L2,K1,V1. K1.ⓑ{I}V1 ⪤[R,#0] L2 →
-      ∃∃K2,V2. K1 ⪤[R,V1] K2 & R K1 V1 V2 & L2 = K2.ⓑ{I}V2.
+      ∀I,L2,K1,V1. K1.ⓑ[I]V1 ⪤[R,#0] L2 →
+      ∃∃K2,V2. K1 ⪤[R,V1] K2 & R K1 V1 V2 & L2 = K2.ⓑ[I]V2.
 #R #I #L2 #K1 #V1 #H elim (rex_inv_zero … H) -H *
 [ #H destruct
 | #Z #Y1 #K2 #X1 #V2 #HK12 #HV12 #H1 #H2 destruct
@@ -162,8 +162,8 @@ lemma rex_inv_zero_pair_sn (R):
 qed-.
 
 lemma rex_inv_zero_pair_dx (R):
-      ∀I,L1,K2,V2. L1 ⪤[R,#0] K2.ⓑ{I}V2 →
-      ∃∃K1,V1. K1 ⪤[R,V1] K2 & R K1 V1 V2 & L1 = K1.ⓑ{I}V1.
+      ∀I,L1,K2,V2. L1 ⪤[R,#0] K2.ⓑ[I]V2 →
+      ∃∃K1,V1. K1 ⪤[R,V1] K2 & R K1 V1 V2 & L1 = K1.ⓑ[I]V1.
 #R #I #L1 #K2 #V2 #H elim (rex_inv_zero … H) -H *
 [ #_ #H destruct
 | #Z #K1 #Y2 #V1 #X2 #HK12 #HV12 #H1 #H2 destruct
@@ -173,8 +173,8 @@ lemma rex_inv_zero_pair_dx (R):
 qed-.
 
 lemma rex_inv_zero_unit_sn (R):
-      ∀I,K1,L2. K1.ⓤ{I} ⪤[R,#0] L2 →
-      â\88\83â\88\83f,K2. ð\9d\90\88â¦\83fâ¦\84 & K1 ⪤[cext2 R,cfull,f] K2 & L2 = K2.â\93¤{I}.
+      ∀I,K1,L2. K1.ⓤ[I] ⪤[R,#0] L2 →
+      â\88\83â\88\83f,K2. ð\9d\90\88â\9dªfâ\9d« & K1 ⪤[cext2 R,cfull,f] K2 & L2 = K2.â\93¤[I].
 #R #I #K1 #L2 #H elim (rex_inv_zero … H) -H *
 [ #H destruct
 | #Z #Y1 #Y2 #X1 #X2 #_ #_ #H destruct
@@ -183,8 +183,8 @@ lemma rex_inv_zero_unit_sn (R):
 qed-.
 
 lemma rex_inv_zero_unit_dx (R):
-      ∀I,L1,K2. L1 ⪤[R,#0] K2.ⓤ{I} →
-      â\88\83â\88\83f,K1. ð\9d\90\88â¦\83fâ¦\84 & K1 ⪤[cext2 R,cfull,f] K2 & L1 = K1.â\93¤{I}.
+      ∀I,L1,K2. L1 ⪤[R,#0] K2.ⓤ[I] →
+      â\88\83â\88\83f,K1. ð\9d\90\88â\9dªfâ\9d« & K1 ⪤[cext2 R,cfull,f] K2 & L1 = K1.â\93¤[I].
 #R #I #L1 #K2 #H elim (rex_inv_zero … H) -H *
 [ #_ #H destruct
 | #Z #Y1 #Y2 #X1 #X2 #_ #_ #_ #H destruct
@@ -193,8 +193,8 @@ lemma rex_inv_zero_unit_dx (R):
 qed-.
 
 lemma rex_inv_lref_bind_sn (R):
-      ∀I1,K1,L2,i. K1.ⓘ{I1} ⪤[R,#↑i] L2 →
-      ∃∃I2,K2. K1 ⪤[R,#i] K2 & L2 = K2.ⓘ{I2}.
+      ∀I1,K1,L2,i. K1.ⓘ[I1] ⪤[R,#↑i] L2 →
+      ∃∃I2,K2. K1 ⪤[R,#i] K2 & L2 = K2.ⓘ[I2].
 #R #I1 #K1 #L2 #i #H elim (rex_inv_lref … H) -H *
 [ #H destruct
 | #Z1 #I2 #Y1 #K2 #Hi #H1 #H2 destruct /2 width=4 by ex2_2_intro/
@@ -202,8 +202,8 @@ lemma rex_inv_lref_bind_sn (R):
 qed-.
 
 lemma rex_inv_lref_bind_dx (R):
-      ∀I2,K2,L1,i. L1 ⪤[R,#↑i] K2.ⓘ{I2} →
-      ∃∃I1,K1. K1 ⪤[R,#i] K2 & L1 = K1.ⓘ{I1}.
+      ∀I2,K2,L1,i. L1 ⪤[R,#↑i] K2.ⓘ[I2] →
+      ∃∃I1,K1. K1 ⪤[R,#i] K2 & L1 = K1.ⓘ[I1].
 #R #I2 #K2 #L1 #i #H elim (rex_inv_lref … H) -H *
 [ #_ #H destruct
 | #I1 #Z2 #K1 #Y2 #Hi #H1 #H2 destruct /2 width=4 by ex2_2_intro/
@@ -211,8 +211,8 @@ lemma rex_inv_lref_bind_dx (R):
 qed-.
 
 lemma rex_inv_gref_bind_sn (R):
-      ∀I1,K1,L2,l. K1.ⓘ{I1} ⪤[R,§l] L2 →
-      ∃∃I2,K2. K1 ⪤[R,§l] K2 & L2 = K2.ⓘ{I2}.
+      ∀I1,K1,L2,l. K1.ⓘ[I1] ⪤[R,§l] L2 →
+      ∃∃I2,K2. K1 ⪤[R,§l] K2 & L2 = K2.ⓘ[I2].
 #R #I1 #K1 #L2 #l #H elim (rex_inv_gref … H) -H *
 [ #H destruct
 | #Z1 #I2 #Y1 #K2 #Hl #H1 #H2 destruct /2 width=4 by ex2_2_intro/
@@ -220,8 +220,8 @@ lemma rex_inv_gref_bind_sn (R):
 qed-.
 
 lemma rex_inv_gref_bind_dx (R):
-      ∀I2,K2,L1,l. L1 ⪤[R,§l] K2.ⓘ{I2} →
-      ∃∃I1,K1. K1 ⪤[R,§l] K2 & L1 = K1.ⓘ{I1}.
+      ∀I2,K2,L1,l. L1 ⪤[R,§l] K2.ⓘ[I2] →
+      ∃∃I1,K1. K1 ⪤[R,§l] K2 & L1 = K1.ⓘ[I1].
 #R #I2 #K2 #L1 #l #H elim (rex_inv_gref … H) -H *
 [ #_ #H destruct
 | #I1 #Z2 #K1 #Y2 #Hl #H1 #H2 destruct /2 width=4 by ex2_2_intro/
@@ -231,13 +231,13 @@ qed-.
 (* Basic forward lemmas *****************************************************)
 
 lemma rex_fwd_zero_pair (R):
-      ∀I,K1,K2,V1,V2. K1.ⓑ{I}V1 ⪤[R,#0] K2.ⓑ{I}V2 → K1 ⪤[R,V1] K2.
+      ∀I,K1,K2,V1,V2. K1.ⓑ[I]V1 ⪤[R,#0] K2.ⓑ[I]V2 → K1 ⪤[R,V1] K2.
 #R #I #K1 #K2 #V1 #V2 #H
 elim (rex_inv_zero_pair_sn … H) -H #Y #X #HK12 #_ #H destruct //
 qed-.
 
 (* Basic_2A1: uses: llpx_sn_fwd_pair_sn llpx_sn_fwd_bind_sn llpx_sn_fwd_flat_sn *)
-lemma rex_fwd_pair_sn (R): ∀I,L1,L2,V,T. L1 ⪤[R,②{I}V.T] L2 → L1 ⪤[R,V] L2.
+lemma rex_fwd_pair_sn (R): ∀I,L1,L2,V,T. L1 ⪤[R,②[I]V.T] L2 → L1 ⪤[R,V] L2.
 #R * [ #p ] #I #L1 #L2 #V #T * #f #Hf #HL
 [ elim (frees_inv_bind … Hf) | elim (frees_inv_flat … Hf) ] -Hf
 /4 width=6 by sle_sex_trans, sor_inv_sle_sn, ex2_intro/
@@ -245,19 +245,19 @@ qed-.
 
 (* Basic_2A1: uses: llpx_sn_fwd_bind_dx llpx_sn_fwd_bind_O_dx *)
 lemma rex_fwd_bind_dx (R):
-      ∀p,I,L1,L2,V1,V2,T. L1 ⪤[R,ⓑ{p,I}V1.T] L2 →
-      R L1 V1 V2 → L1.ⓑ{I}V1 ⪤[R,T] L2.ⓑ{I}V2.
+      ∀p,I,L1,L2,V1,V2,T. L1 ⪤[R,ⓑ[p,I]V1.T] L2 →
+      R L1 V1 V2 → L1.ⓑ[I]V1 ⪤[R,T] L2.ⓑ[I]V2.
 #R #p #I #L1 #L2 #V1 #V2 #T #H #HV elim (rex_inv_bind … H HV) -H -HV //
 qed-.
 
 (* Basic_2A1: uses: llpx_sn_fwd_flat_dx *)
-lemma rex_fwd_flat_dx (R): ∀I,L1,L2,V,T. L1 ⪤[R,ⓕ{I}V.T] L2 → L1 ⪤[R,T] L2.
+lemma rex_fwd_flat_dx (R): ∀I,L1,L2,V,T. L1 ⪤[R,ⓕ[I]V.T] L2 → L1 ⪤[R,T] L2.
 #R #I #L1 #L2 #V #T #H elim (rex_inv_flat … H) -H //
 qed-.
 
 lemma rex_fwd_dx (R):
-      ∀I2,L1,K2,T. L1 ⪤[R,T] K2.ⓘ{I2} →
-      ∃∃I1,K1. L1 = K1.ⓘ{I1}.
+      ∀I2,L1,K2,T. L1 ⪤[R,T] K2.ⓘ[I2] →
+      ∃∃I1,K1. L1 = K1.ⓘ[I1].
 #R #I2 #L1 #K2 #T * #f elim (pn_split f) * #g #Hg #_ #Hf destruct
 [ elim (sex_inv_push2 … Hf) | elim (sex_inv_next2 … Hf) ] -Hf #I1 #K1 #_ #_ #H destruct
 /2 width=3 by ex1_2_intro/
@@ -265,12 +265,12 @@ qed-.
 
 (* Basic properties *********************************************************)
 
-lemma rex_atom (R): ∀I. ⋆ ⪤[R,⓪{I}] ⋆.
+lemma rex_atom (R): ∀I. ⋆ ⪤[R,⓪[I]] ⋆.
 #R * /3 width=3 by frees_sort, frees_atom, frees_gref, sex_atom, ex2_intro/
 qed.
 
 lemma rex_sort (R):
-      ∀I1,I2,L1,L2,s. L1 ⪤[R,⋆s] L2 → L1.ⓘ{I1} ⪤[R,⋆s] L2.ⓘ{I2}.
+      ∀I1,I2,L1,L2,s. L1 ⪤[R,⋆s] L2 → L1.ⓘ[I1] ⪤[R,⋆s] L2.ⓘ[I2].
 #R #I1 #I2 #L1 #L2 #s * #f #Hf #H12
 lapply (frees_inv_sort … Hf) -Hf
 /4 width=3 by frees_sort, sex_push, isid_push, ex2_intro/
@@ -278,31 +278,31 @@ qed.
 
 lemma rex_pair (R):
       ∀I,L1,L2,V1,V2. L1 ⪤[R,V1] L2 →
-      R L1 V1 V2 → L1.ⓑ{I}V1 ⪤[R,#0] L2.ⓑ{I}V2.
+      R L1 V1 V2 → L1.ⓑ[I]V1 ⪤[R,#0] L2.ⓑ[I]V2.
 #R #I1 #I2 #L1 #L2 #V1 *
 /4 width=3 by ext2_pair, frees_pair, sex_next, ex2_intro/
 qed.
 
 lemma rex_unit (R):
-      â\88\80f,I,L1,L2. ð\9d\90\88â¦\83fâ¦\84 → L1 ⪤[cext2 R,cfull,f] L2 →
-      L1.ⓤ{I} ⪤[R,#0] L2.ⓤ{I}.
+      â\88\80f,I,L1,L2. ð\9d\90\88â\9dªfâ\9d« → L1 ⪤[cext2 R,cfull,f] L2 →
+      L1.ⓤ[I] ⪤[R,#0] L2.ⓤ[I].
 /4 width=3 by frees_unit, sex_next, ext2_unit, ex2_intro/ qed.
 
 lemma rex_lref (R):
-      ∀I1,I2,L1,L2,i. L1 ⪤[R,#i] L2 → L1.ⓘ{I1} ⪤[R,#↑i] L2.ⓘ{I2}.
+      ∀I1,I2,L1,L2,i. L1 ⪤[R,#i] L2 → L1.ⓘ[I1] ⪤[R,#↑i] L2.ⓘ[I2].
 #R #I1 #I2 #L1 #L2 #i * /3 width=3 by sex_push, frees_lref, ex2_intro/
 qed.
 
 lemma rex_gref (R):
-      ∀I1,I2,L1,L2,l. L1 ⪤[R,§l] L2 → L1.ⓘ{I1} ⪤[R,§l] L2.ⓘ{I2}.
+      ∀I1,I2,L1,L2,l. L1 ⪤[R,§l] L2 → L1.ⓘ[I1] ⪤[R,§l] L2.ⓘ[I2].
 #R #I1 #I2 #L1 #L2 #l * #f #Hf #H12
 lapply (frees_inv_gref … Hf) -Hf
 /4 width=3 by frees_gref, sex_push, isid_push, ex2_intro/
 qed.
 
 lemma rex_bind_repl_dx (R):
-      ∀I,I1,L1,L2,T. L1.ⓘ{I} ⪤[R,T] L2.ⓘ{I1} →
-      ∀I2. cext2 R L1 I I2 → L1.ⓘ{I} ⪤[R,T] L2.ⓘ{I2}.
+      ∀I,I1,L1,L2,T. L1.ⓘ[I] ⪤[R,T] L2.ⓘ[I1] →
+      ∀I2. cext2 R L1 I I2 → L1.ⓘ[I] ⪤[R,T] L2.ⓘ[I2].
 #R #I #I1 #L1 #L2 #T * #f #Hf #HL12 #I2 #HR
 /3 width=5 by sex_pair_repl, ex2_intro/
 qed-.
@@ -316,15 +316,15 @@ qed-.
 
 lemma rex_isid (R1) (R2):
       ∀L1,L2,T1,T2.
-      (â\88\80f. L1 â\8a¢ ð\9d\90\85+â¦\83T1â¦\84 â\89\98 f â\86\92 ð\9d\90\88â¦\83fâ¦\84) →
-      (â\88\80f. ð\9d\90\88â¦\83fâ¦\84 â\86\92 L1 â\8a¢ ð\9d\90\85+â¦\83T2â¦\84 ≘ f) →
+      (â\88\80f. L1 â\8a¢ ð\9d\90\85+â\9dªT1â\9d« â\89\98 f â\86\92 ð\9d\90\88â\9dªfâ\9d«) →
+      (â\88\80f. ð\9d\90\88â\9dªfâ\9d« â\86\92 L1 â\8a¢ ð\9d\90\85+â\9dªT2â\9d« ≘ f) →
       L1 ⪤[R1,T1] L2 → L1 ⪤[R2,T2] L2.
 #R1 #R2 #L1 #L2 #T1 #T2 #H1 #H2 *
 /4 width=7 by sex_co_isid, ex2_intro/
 qed-.
 
 lemma rex_unit_sn (R1) (R2):
-      ∀I,K1,L2. K1.ⓤ{I} ⪤[R1,#0] L2 → K1.ⓤ{I} ⪤[R2,#0] L2.
+      ∀I,K1,L2. K1.ⓤ[I] ⪤[R1,#0] L2 → K1.ⓤ[I] ⪤[R2,#0] L2.
 #R1 #R2 #I #K1 #L2 #H
 elim (rex_inv_zero_unit_sn … H) -H #f #K2 #Hf #HK12 #H destruct
 /3 width=7 by rex_unit, sex_co_isid/