- degree assignment, static type assignment, iterated static type

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / static / ssta_ssta.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/ssta_ssta.ma b/matita/matita/contribs/lambdadelta/basic_2/static/ssta_ssta.ma
index 8cc03442d4c2007f07dce7021675b03a7a7405b3..34d6bb0108f2e6c199ce81afce69b97ddc719178 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/ssta_ssta.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/ssta_ssta.ma
@@ -12,46 +12,40 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "basic_2/static/da_da.ma".
 include "basic_2/static/ssta_lift.ma".
 
 (* STRATIFIED STATIC TYPE ASSIGNMENT ON TERMS *******************************)
 
+(* Advanced inversion lemmas ************************************************)
+
+lemma ssta_inv_refl_pos: ∀h,g,G,L,T,l.  ⦃G, L⦄ ⊢ T ▪[h, g] l+1 → ⦃G, L⦄ ⊢ T •[h, g] T → ⊥.
+#h #g #G #L #T #l #H1T #HTT
+lapply (ssta_da_conf … HTT … H1T) -HTT <minus_plus_m_m #H2T
+lapply (da_mono … H2T … H1T) -h -G -L -T #H
+elim (plus_xySz_x_false 0 l 0) //
+qed-.
+
 (* Main properties **********************************************************)
 
-(* Note: apparently this was missing in basic_1 *)
-theorem ssta_mono: ∀h,g,G,L,T,U1,l1. ⦃G, L⦄ ⊢ T •[h, g] ⦃l1, U1⦄ →
-                   ∀U2,l2. ⦃G, L⦄ ⊢ T •[h, g] ⦃l2, U2⦄ → l1 = l2 ∧ U1 = U2.
-#h #g #G #L #T #U1 #l1 #H elim H -G -L -T -U1 -l1
-[ #G #L #k #l #Hkl #X #l2 #H
-  elim (ssta_inv_sort1 … H) -H #Hkl2 #H destruct
-  >(deg_mono … Hkl2 … Hkl) -g -L -l2 /2 width=1/
-| #G #L #K #V #W #U1 #i #l1 #HLK #_ #HWU1 #IHVW #U2 #l2 #H
-  elim (ssta_inv_lref1 … H) -H * #K0 #V0 #W0 [2: #l0] #HLK0 #HVW0 #HW0U2
+theorem ssta_mono: ∀h,g,G,L. singlevalued … (ssta h g G L).
+#h #g #G #L #T #U1 #H elim H -G -L -T -U1
+[ #G #L #k #X #H >(ssta_inv_sort1 … H) -X //
+| #G #L #K #V #U1 #W #i #HLK #_ #HWU1 #IHVW #U2 #H
+  elim (ssta_inv_lref1 … H) -H * #K0 #V0 #W0 #HLK0 #HVW0 #HW0U2
   lapply (ldrop_mono … HLK0 … HLK) -HLK -HLK0 #H destruct
-  lapply (IHVW … HVW0) -IHVW -HVW0 * #H1 #H2 destruct
-  >(lift_mono … HWU1 … HW0U2) -W0 -U1 /2 width=1/
-| #G #L #K #W #V #U1 #i #l1 #HLK #_ #HWU1 #IHWV #U2 #l2 #H
-  elim (ssta_inv_lref1 … H) -H * #K0 #W0 #V0 [2: #l0 ] #HLK0 #HWV0 #HV0U2
+  lapply (IHVW … HVW0) -IHVW -HVW0 #H destruct
+  >(lift_mono … HWU1 … HW0U2) -W0 -U1 //
+| #G #L #K #W #U1 #l #i #HLK #HWl #HWU1 #U2 #H
+  elim (ssta_inv_lref1 … H) -H * #K0 #W0 #l0 #HLK0 #HWl0 #HW0U2
   lapply (ldrop_mono … HLK0 … HLK) -HLK -HLK0 #H destruct
-  lapply (IHWV … HWV0) -IHWV -HWV0 * #H1 #H2 destruct
-  >(lift_mono … HWU1 … HV0U2) -W -U1 /2 width=1/
-| #a #I #G #L #V #T #U1 #l1 #_ #IHTU1 #X #l2 #H
-  elim (ssta_inv_bind1 … H) -H #U2 #HTU2 #H destruct
-  elim (IHTU1 … HTU2) -T /3 width=1/
-| #G #L #V #T #U1 #l1 #_ #IHTU1 #X #l2 #H
-  elim (ssta_inv_appl1 … H) -H #U2 #HTU2 #H destruct
-  elim (IHTU1 … HTU2) -T /3 width=1/
-| #G #L #W1 #T #U1 #l1 #_ #IHTU1 #U2 #l2 #H
-  lapply (ssta_inv_cast1 … H) -H #HTU2
-  elim (IHTU1 … HTU2) -T /2 width=1/
+  lapply (da_mono … HWl0 … HWl) -HWl0 #H destruct
+  >(lift_mono … HWU1 … HW0U2) -W -U1 //
+| #a #I #G #L #V #T #U1 #_ #IHTU1 #X #H
+  elim (ssta_inv_bind1 … H) -H #U2 #HTU2 #H destruct /3 width=1/
+| #G #L #V #T #U1 #_ #IHTU1 #X #H
+  elim (ssta_inv_appl1 … H) -H #U2 #HTU2 #H destruct /3 width=1/
+| #G #L #W #T #U1 #_ #IHTU1 #U2 #H
+  lapply (ssta_inv_cast1 … H) -H /2 width=1/
 ]
 qed-.
-
-(* Advanced inversion lemmas ************************************************)
-
-lemma ssta_inv_refl_pos: ∀h,g,G,L,T,l. ⦃G, L⦄ ⊢ T •[h, g] ⦃l+1, T⦄ → ⊥.
-#h #g #G #L #T #l #HTT
-elim (ssta_fwd_correct … HTT) <minus_plus_m_m #U #HTU
-elim (ssta_mono … HTU … HTT) -h -L #H #_ -T -U
-elim (plus_xySz_x_false 0 l 0 ?) //
-qed-.