milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / etc / snv / snv_preserve.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/etc/snv/snv_preserve.etc b/matita/matita/contribs/lambdadelta/basic_2A/etc/snv/snv_preserve.etc
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/basic_2A/etc/snv/snv_preserve.etc
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+lemma da_cpcs: ∀h,g,G,L,T1. ⦃G, L⦄ ⊢ T1 ¡[h, g] →
+               ∀T2. ⦃G, L⦄ ⊢ T2 ¡[h, g] →
+               ∀l1. ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 → ∀l2. ⦃G, L⦄ ⊢ T2 ▪[h, g] l2 →
+               ⦃G, L⦄ ⊢ T1 ⬌* T2 → l1 = l2.
+#h #g #G #L #T1 #HT1 #T2 #HT2 #l1 #Hl1 #l2 #Hl2 #H
+elim (cpcs_inv_cprs … H) -H /3 width=12 by da_cprs_lpr, da_mono/
+qed-.
+
+lemma sta_cpr_lpr: ∀h,g,G,L1,T1. ⦃G, L1⦄ ⊢ T1 ¡[h, g] →
+                   ∀l. ⦃G, L1⦄ ⊢ T1 ▪[h, g] l+1 →
+                   ∀U1. ⦃G, L1⦄ ⊢ T1 •[h] U1 →
+                   ∀T2. ⦃G, L1⦄ ⊢ T1 ➡ T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 →
+                   ∃∃U2. ⦃G, L2⦄ ⊢ T2 •[h] U2 & ⦃G, L2⦄ ⊢ U1 ⬌* U2.
+#h #g #G #L1 #T1 #HT1 #l #Hl #U1 #HTU1 #T2 #HT12 #L2 #HL12
+elim (lstas_cpr_lpr  … 1 … Hl U1 … HT12 … HL12) -Hl -HT12 -HL12
+/3 width=3 by lstas_inv_SO, sta_lstas, ex2_intro/
+qed-.
+
+lemma snv_sta: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, g] →
+               ∀l. ⦃G, L⦄ ⊢ T ▪[h, g] l+1 →
+               ∀U. ⦃G, L⦄ ⊢ T •[h] U → ⦃G, L⦄ ⊢ U ¡[h, g].
+/3 width=7 by lstas_inv_SO, sta_lstas, snv_lstas/ qed-.
+
+lemma lstas_cpds: ∀h,g,G,L,T1. ⦃G, L⦄ ⊢ T1 ¡[h, g] →
+                  ∀l1,l2. l2 ≤ l1 → ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 →
+                  ∀U1. ⦃G, L⦄ ⊢ T1 •*[h, l2] U1 → ∀T2. ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2 →
+                  ∃∃U2,l. l ≤ l2 & ⦃G, L⦄ ⊢ T2 •*[h, l] U2 & ⦃G, L⦄ ⊢ U1 •*⬌*[h, g] U2.
+#h #g #G #L #T1 #HT1 #l1 #l2 #Hl21 #Hl1 #U1 #HTU1 #T2 * #T #l0 #l #Hl0 #H #HT1T #HTT2
+lapply (da_mono … H … Hl1) -H #H destruct
+lapply (lstas_da_conf … HTU1 … Hl1) #Hl12
+elim (le_or_ge l2 l) #Hl2
+[ lapply (lstas_conf_le … HTU1 … HT1T) -HT1T //
+  /5 width=11 by cpds_cpes_dx, monotonic_le_minus_l, ex3_2_intro, ex4_3_intro/
+| lapply (lstas_da_conf … HT1T … Hl1) #Hl1l
+  lapply (lstas_conf_le … HT1T … HTU1) -HTU1 // #HTU1
+  elim (lstas_cprs_lpr … Hl1l … HTU1 … HTT2 L) -Hl1l -HTU1 -HTT2
+  /3 width=7 by snv_lstas, cpcs_cpes, monotonic_le_minus_l, ex3_2_intro/
+]
+qed-.
+
+lemma cpds_cpr_lpr: ∀h,g,G,L1,T1. ⦃G, L1⦄ ⊢ T1 ¡[h, g] →
+                    ∀U1. ⦃G, L1⦄ ⊢ T1 •*➡*[h, g] U1 →
+                    ∀T2. ⦃G, L1⦄ ⊢ T1 ➡ T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 →
+                    ∃∃U2. ⦃G, L2⦄ ⊢ T2 •*➡*[h, g] U2 & ⦃G, L2⦄ ⊢ U1 ➡* U2.
+#h #g #G #L1 #T1 #HT1 #U1 * #W1 #l1 #l2 #Hl21 #Hl1 #HTW1 #HWU1 #T2 #HT12 #L2 #HL12
+elim (lstas_cpr_lpr … Hl1 … HTW1 … HT12 … HL12) // #W2 #HTW2 #HW12
+lapply (da_cpr_lpr … Hl1 … HT12 … HL12) // -T1
+lapply (lpr_cprs_conf … HL12 … HWU1) -L1 #HWU1
+lapply (cpcs_canc_sn … HW12 HWU1) -W1 #H
+elim (cpcs_inv_cprs … H) -H /3 width=7 by ex4_3_intro, ex2_intro/
+qed-.
+
+(* Note: missing da_scpds_lpr, da_scpes *)
+
+lemma scpds_cpr_lpr: ∀h,g,G,L1,T1. ⦃G, L1⦄ ⊢ T1 ¡[h, g] →
+                     ∀U1,l. ⦃G, L1⦄ ⊢ T1 •*➡*[h, g, l] U1 →
+                     ∀T2. ⦃G, L1⦄ ⊢ T1 ➡ T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 →
+                     ∃∃U2. ⦃G, L2⦄ ⊢ T2 •*➡*[h, g, l] U2 & ⦃G, L2⦄ ⊢ U1 ➡* U2.
+#h #g #G #L1 #T1 #HT1 #U1 #l2 * #W1 #l1 #Hl21 #HTl1 #HTW1 #HWU1 #T2 #HT12 #L2 #HL12
+elim (lstas_cpr_lpr … HTl1 … HTW1 … HT12 … HL12) // #W2 #HTW2 #HW12
+lapply (da_cpr_lpr … HTl1 … HT12 … HL12) // -T1
+lapply (lpr_cprs_conf … HL12 … HWU1) -L1 #HWU1
+lapply (cpcs_canc_sn … HW12 HWU1) -W1 #H
+elim (cpcs_inv_cprs … H) -H /3 width=6 by ex4_2_intro, ex2_intro/
+qed-.
+
+lemma scpes_cpr_lpr: ∀h,g,G,L1,T1. ⦃G, L1⦄ ⊢ T1 ¡[h, g] →
+                     ∀T2. ⦃G, L1⦄ ⊢ T2 ¡[h, g] →
+                     ∀l1,l2. ⦃G, L1⦄ ⊢ T1 •*⬌*[h, g, l1, l2] T2 →
+                     ∀U1. ⦃G, L1⦄ ⊢ T1 ➡ U1 → ∀U2. ⦃G, L1⦄ ⊢ T2 ➡ U2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 →
+                     ⦃G, L2⦄ ⊢ U1 •*⬌*[h, g, l1, l2] U2.
+#h #g #G #L1 #T1 #HT1 #T2 #HT2 #l1 #l2 * #T0 #HT10 #HT20 #U1 #HTU1 #U2 #HTU2 #L2 #HL12
+elim (scpds_cpr_lpr … HT10 … HTU1 … HL12) -HT10 -HTU1 // #X1 #HUX1 #H1
+elim (scpds_cpr_lpr … HT20 … HTU2 … HL12) -HT20 -HTU2 // #X2 #HUX2 #H2
+elim (cprs_conf … H1 … H2) -T0 /3 width=5 by scpds_div, scpds_cprs_trans/
+qed-.
+
+(* Note: missing lstas_scpds, scpes_le *)