partial commit: just the components before "static" ...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / unfold / sstas.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/unfold/sstas.ma b/matita/matita/contribs/lambdadelta/basic_2/unfold/sstas.ma
index 6a68fb61bc62bf241dea362a41f2ecc20787c593..191da2befc777824140c27ae314f00c0b90f908e 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/unfold/sstas.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/unfold/sstas.ma
@@ -28,20 +28,20 @@ interpretation "iterated stratified static type assignment (term)"
 
 lemma sstas_ind: ∀h,g,L,T. ∀R:predicate term.
                  R T → (
-                    ∀U1,U2,l. ⦃h, L⦄ ⊢ T •* [g] U1 →  ⦃h, L⦄ ⊢ U1 •[g] ⦃l+1, U2⦄ →
+                    ∀U1,U2,l. ⦃G, L⦄ ⊢ T •* [h, g] U1 →  ⦃G, L⦄ ⊢ U1 •[h, g] ⦃l+1, U2⦄ →
                     R U1 → R U2
                  ) →
-                 ∀U. ⦃h, L⦄ ⊢ T •*[g] U → R U.
+                 ∀U. ⦃G, L⦄ ⊢ T •*[h, g] U → R U.
 #h #g #L #T #R #IH1 #IH2 #U #H elim H -U //
 #U1 #U2 #H * /2 width=5/
 qed-.
 
 lemma sstas_ind_dx: ∀h,g,L,U2. ∀R:predicate term.
                     R U2 → (
-                       ∀T,U1,l. ⦃h, L⦄ ⊢ T •[g] ⦃l+1, U1⦄ → ⦃h, L⦄ ⊢ U1 •* [g] U2 →
+                       ∀T,U1,l. ⦃G, L⦄ ⊢ T •[h, g] ⦃l+1, U1⦄ → ⦃G, L⦄ ⊢ U1 •* [h, g] U2 →
                        R U1 → R T
                     ) →
-                    ∀T. ⦃h, L⦄ ⊢ T •*[g] U2 → R T.
+                    ∀T. ⦃G, L⦄ ⊢ T •*[h, g] U2 → R T.
 #h #g #L #U2 #R #IH1 #IH2 #T #H @(star_ind_l … T H) -T //
 #T #T0 * /2 width=5/
 qed-.
@@ -51,30 +51,30 @@ qed-.
 lemma sstas_refl: ∀h,g,L. reflexive … (sstas h g L).
 // qed.
 
-lemma ssta_sstas: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g] ⦃l+1, U⦄ → ⦃h, L⦄ ⊢ T •*[g] U.
+lemma ssta_sstas: ∀h,g,L,T,U,l. ⦃G, L⦄ ⊢ T •[h, g] ⦃l+1, U⦄ → ⦃G, L⦄ ⊢ T •*[h, g] U.
 /3 width=2 by R_to_star, ex_intro/ qed. (**) (* auto fails without trace *)
 
-lemma sstas_strap1: ∀h,g,L,T1,T2,U2,l. ⦃h, L⦄ ⊢ T1 •*[g] T2 → ⦃h, L⦄ ⊢ T2 •[g] ⦃l+1, U2⦄ →
-                    ⦃h, L⦄ ⊢ T1 •*[g] U2.
+lemma sstas_strap1: ∀h,g,L,T1,T2,U2,l. ⦃G, L⦄ ⊢ T1 •*[h, g] T2 → ⦃G, L⦄ ⊢ T2 •[h, g] ⦃l+1, U2⦄ →
+                    ⦃G, L⦄ ⊢ T1 •*[h, g] U2.
 /3 width=4 by sstep, ex_intro/ (**) (* auto fails without trace *)
 qed.
 
-lemma sstas_strap2: ∀h,g,L,T1,U1,U2,l. ⦃h, L⦄ ⊢ T1 •[g] ⦃l+1, U1⦄ → ⦃h, L⦄ ⊢ U1 •*[g] U2 →
-                    ⦃h, L⦄ ⊢ T1 •*[g] U2.
+lemma sstas_strap2: ∀h,g,L,T1,U1,U2,l. ⦃G, L⦄ ⊢ T1 •[h, g] ⦃l+1, U1⦄ → ⦃G, L⦄ ⊢ U1 •*[h, g] U2 →
+                    ⦃G, L⦄ ⊢ T1 •*[h, g] U2.
 /3 width=3 by star_compl, ex_intro/ (**) (* auto fails without trace *)
 qed.
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma sstas_inv_bind1: ∀h,g,a,I,L,Y,X,U. ⦃h, L⦄ ⊢ ⓑ{a,I}Y.X •*[g] U →
-                       ∃∃Z. ⦃h, L.ⓑ{I}Y⦄ ⊢ X •*[g] Z & U = ⓑ{a,I}Y.Z.
+lemma sstas_inv_bind1: ∀h,g,a,I,L,Y,X,U. ⦃G, L⦄ ⊢ ⓑ{a,I}Y.X •*[h, g] U →
+                       ∃∃Z. ⦃h, L.ⓑ{I}Y⦄ ⊢ X •*[h, g] Z & U = ⓑ{a,I}Y.Z.
 #h #g #a #I #L #Y #X #U #H @(sstas_ind … H) -U /2 width=3/
 #T #U #l #_ #HTU * #Z #HXZ #H destruct
 elim (ssta_inv_bind1 … HTU) -HTU #Z0 #HZ0 #H destruct /3 width=4/
 qed-.
 
-lemma sstas_inv_appl1: ∀h,g,L,Y,X,U. ⦃h, L⦄ ⊢ ⓐY.X •*[g] U →
-                       ∃∃Z. ⦃h, L⦄ ⊢ X •*[g] Z & U = ⓐY.Z.
+lemma sstas_inv_appl1: ∀h,g,L,Y,X,U. ⦃G, L⦄ ⊢ ⓐY.X •*[h, g] U →
+                       ∃∃Z. ⦃G, L⦄ ⊢ X •*[h, g] Z & U = ⓐY.Z.
 #h #g #L #Y #X #U #H @(sstas_ind … H) -U /2 width=3/
 #T #U #l #_ #HTU * #Z #HXZ #H destruct
 elim (ssta_inv_appl1 … HTU) -HTU #Z0 #HZ0 #H destruct /3 width=4/