partial commit in static_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / relocation / drops_sex.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/drops_sex.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/drops_sex.ma
index aeff28ceeda71426dc782d6ea008e1d5b2e11c4a..18017d88ae41fcce0471faaf4616ddc7d0a98620 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/drops_sex.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/drops_sex.ma
@@ -26,19 +26,19 @@ lemma sex_co_dropable_sn (RN) (RP):
 [ #f #Hf #_ #f2 #X #H #f1 #Hf2 >(sex_inv_atom1 … H) -X
   /4 width=3 by sex_atom, drops_atom, ex2_intro/
 | #f #I1 #L1 #K1 #_ #IH #Hf #f2 #X #H #f1 #Hf2
-  elim (coafter_inv_nxx … Hf2) -Hf2 [2,3: // ] #g2 #Hg2 #H2 destruct
+  elim (pr_coafter_inv_next_sn … Hf2) -Hf2 [2,3: // ] #g2 #Hg2 #H2 destruct
   elim (sex_inv_push1 … H) -H #I2 #L2 #HL12 #HI12 #H destruct
   elim (IH … HL12 … Hg2) -g2
-  /3 width=3 by isuni_inv_next, drops_drop, ex2_intro/
+  /3 width=3 by pr_isu_inv_next, drops_drop, ex2_intro/
 | #f #I1 #J1 #L1 #K1 #HLK #HJI1 #IH #Hf #f2 #X #H #f1 #Hf2
-  lapply (isuni_inv_push … Hf ??) -Hf [3: |*: // ] #Hf
+  lapply (pr_isu_inv_push … Hf ??) -Hf [3: |*: // ] #Hf
   lapply (drops_fwd_isid … HLK … Hf) -HLK #H0 destruct
   lapply (liftsb_fwd_isid … HJI1 … Hf) -HJI1 #H0 destruct
-  elim (coafter_inv_pxx … Hf2) -Hf2 [1,3:* |*: // ] #g1 #g2 #Hg2 #H1 #H2 destruct
+  elim (pr_coafter_inv_push_sn … Hf2) -Hf2 [1,3:* |*: // ] #g1 #g2 #Hg2 #H1 #H2 destruct
   [ elim (sex_inv_push1 … H) | elim (sex_inv_next1 … H) ] -H #I2 #L2 #HL12 #HI12 #H destruct
-  elim (IH … HL12 … Hg2) -g2 -IH /2 width=1 by isuni_isid/ #K2 #HK12 #HLK2
+  elim (IH … HL12 … Hg2) -g2 -IH /2 width=1 by pr_isu_isi/ #K2 #HK12 #HLK2
   lapply (drops_fwd_isid … HLK2 … Hf) -HLK2 #H0 destruct
-  /4 width=3 by drops_refl, sex_next, sex_push, isid_push, ex2_intro/
+  /4 width=3 by drops_refl, sex_next, sex_push, pr_isi_push, ex2_intro/
 ]
 qed-.
 
@@ -49,13 +49,13 @@ lemma sex_liftable_co_dedropable_bi (RN) (RP):
       f ~⊚ f1 ≘ f2 → L1 ⪤[RN,RP,f2] L2.
 #RN #RP #HRN #HRP #f2 #L1 #L2 #H elim H -f2 -L1 -L2 //
 #g2 #I1 #I2 #L1 #L2 #HL12 #HI12 #IH #f1 #Y1 #Y2 #HK12 #b #f #HY1 #HY2 #H
-[ elim (coafter_inv_xxn … H) [ |*: // ] -H #g #g1 #Hg2 #H1 #H2 destruct
+[ elim (pr_coafter_inv_next … H) [ |*: // ] -H #g #g1 #Hg2 #H1 #H2 destruct
   elim (drops_inv_skip1 … HY1) -HY1 #J1 #K1 #HLK1 #HJI1 #H destruct
   elim (drops_inv_skip1 … HY2) -HY2 #J2 #K2 #HLK2 #HJI2 #H destruct
   elim (sex_inv_next … HK12) -HK12 #HK12 #HJ12
   elim (HRN … HJ12 … HLK1 … HJI1) -HJ12 -HJI1 #Z #Hz
   >(liftsb_mono … Hz … HJI2) -Z /3 width=9 by sex_next/
-| elim (coafter_inv_xxp … H) [1,2: |*: // ] -H *
+| elim (pr_coafter_inv_push … H) [1,2: |*: // ] -H *
   [ #g #g1 #Hg2 #H1 #H2 destruct
     elim (drops_inv_skip1 … HY1) -HY1 #J1 #K1 #HLK1 #HJI1 #H destruct
     elim (drops_inv_skip1 … HY2) -HY2 #J2 #K2 #HLK2 #HJI2 #H destruct
@@ -78,11 +78,11 @@ lemma sex_liftable_co_dedropable_sn (RN) (RP):
 [ #f #Hf #X #f1 #H #f2 #Hf2 >(sex_inv_atom1 … H) -X
   /4 width=4 by drops_atom, sex_atom, ex3_intro/
 | #f #I1 #L1 #K1 #_ #IHLK1 #K2 #f1 #HK12 #f2 #Hf2
-  elim (coafter_inv_nxx … Hf2) -Hf2 [2,3: // ] #g2 #Hg2 #H destruct
+  elim (pr_coafter_inv_next_sn … Hf2) -Hf2 [2,3: // ] #g2 #Hg2 #H destruct
   elim (IHLK1 … HK12 … Hg2) -K1
   /3 width=6 by drops_drop, sex_next, sex_push, ex3_intro/
 | #f #I1 #J1 #L1 #K1 #HLK1 #HJI1 #IHLK1 #X #f1 #H #f2 #Hf2
-  elim (coafter_inv_pxx … Hf2) -Hf2 [1,3: * |*: // ] #g1 #g2 #Hg2 #H1 #H2 destruct
+  elim (pr_coafter_inv_push_sn … Hf2) -Hf2 [1,3: * |*: // ] #g1 #g2 #Hg2 #H1 #H2 destruct
   [ elim (sex_inv_push1 … H) | elim (sex_inv_next1 … H) ] -H #J2 #K2 #HK12 #HJ12 #H destruct
   [ elim (H2RP … HJ12 … HLK1 … HJI1) | elim (H2RN … HJ12 … HLK1 … HJI1) ] -J1
   elim (IHLK1 … HK12 … Hg2) -K1
@@ -98,18 +98,18 @@ fact sex_dropable_dx_aux (RN) (RP):
 [ #f #Hf #_ #f2 #X #H #f1 #Hf2 lapply (sex_inv_atom2 … H) -H
   #H destruct /4 width=3 by sex_atom, drops_atom, ex2_intro/
 | #f #I2 #L2 #K2 #_ #IH #Hf #f2 #X #HX #f1 #Hf2
-  elim (coafter_inv_nxx … Hf2) -Hf2 [2,3: // ] #g2 #Hg2 #H destruct
+  elim (pr_coafter_inv_next_sn … Hf2) -Hf2 [2,3: // ] #g2 #Hg2 #H destruct
   elim (sex_inv_push2 … HX) -HX #I1 #L1 #HL12 #HI12 #H destruct
   elim (IH … HL12 … Hg2) -L2 -I2 -g2
-  /3 width=3 by drops_drop, isuni_inv_next, ex2_intro/
+  /3 width=3 by drops_drop, pr_isu_inv_next, ex2_intro/
 | #f #I2 #J2 #L2 #K2 #_ #HJI2 #IH #Hf #f2 #X #HX #f1 #Hf2
-  elim (coafter_inv_pxx … Hf2) -Hf2 [1,3: * |*: // ] #g1 #g2 #Hg2 #H1 #H2 destruct
+  elim (pr_coafter_inv_push_sn … Hf2) -Hf2 [1,3: * |*: // ] #g1 #g2 #Hg2 #H1 #H2 destruct
   [ elim (sex_inv_push2 … HX) | elim (sex_inv_next2 … HX) ] -HX #I1 #L1 #HL12 #HI12 #H destruct
-  elim (IH … HL12 … Hg2) -L2 -g2 /2 width=3 by isuni_fwd_push/ #K1 #HLK1 #HK12
-  lapply (isuni_inv_push … Hf ??) -Hf [3,6: |*: // ] #Hf
+  elim (IH … HL12 … Hg2) -L2 -g2 /2 width=3 by pr_isu_fwd_push/ #K1 #HLK1 #HK12
+  lapply (pr_isu_inv_push … Hf ??) -Hf [3,6: |*: // ] #Hf
   lapply (liftsb_fwd_isid … HJI2 … Hf) #H destruct -HJI2
   lapply (drops_fwd_isid … HLK1 … Hf) #H destruct -HLK1
-  /4 width=5 by sex_next, sex_push, drops_refl, isid_push, ex2_intro/
+  /4 width=5 by sex_next, sex_push, drops_refl, pr_isi_push, ex2_intro/
 ]
 qed-.
 
@@ -205,16 +205,16 @@ lemma sex_sdj_split_dx (R1) (R2) (RP):
 [ #f1 #_ #L2 #H #f2 #_
   lapply (sex_inv_atom1 … H) -H #H destruct
   /2 width=3 by sex_atom, ex2_intro/
-| #K1 #I1 #IH #f1 elim (pn_split f1) * #g1 #H destruct
+| #K1 #I1 #IH #f1 elim (pr_map_split_tl f1) * #g1 #H destruct
   #HR #L2 #H #f2 #Hf
   [ elim (sex_inv_push1 … H) -H #I2 #K2 #HK12 #HI12 #H destruct
-    elim (sdj_inv_px … Hf ??) -Hf [1,3: * |*: // ] #g2 #Hg #H destruct
+    elim (pr_sdj_inv_push_sn … Hf ??) -Hf [1,3: * |*: // ] #g2 #Hg #H destruct
     elim (IH … HK12 … Hg) -IH -HK12 -Hg
     [1,3: /3 width=5 by sex_next, sex_push, ex2_intro/
     |2,4: /3 width=3 by drops_drop/
     ]
   | elim (sex_inv_next1 … H) -H #I2 #K2 #HK12 #HI12 #H destruct
-    elim (sdj_inv_nx … Hf ??) -Hf [|*: // ] #g2 #Hg #H destruct
+    elim (pr_sdj_inv_next_sn … Hf ??) -Hf [|*: // ] #g2 #Hg #H destruct
     elim (IH … HK12 … Hg) -IH -HK12 -Hg
     [ /5 width=11 by sex_next, sex_push, drops_refl, ex2_intro/
     | /3 width=3 by drops_drop/