X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fapps_2%2Fexamples%2Fex_cpr_omega.ma;h=0f07f5997f922e4304c7a998f20ce1fa11806b27;hp=6490866044512e6f2b8587d171e2676e583953d7;hb=bd53c4e895203eb049e75434f638f26b5a161a2b;hpb=3b7b8afcb429a60d716d5226a5b6ab0d003228b1 diff --git a/matita/matita/contribs/lambdadelta/apps_2/examples/ex_cpr_omega.ma b/matita/matita/contribs/lambdadelta/apps_2/examples/ex_cpr_omega.ma index 649086604..0f07f5997 100644 --- a/matita/matita/contribs/lambdadelta/apps_2/examples/ex_cpr_omega.ma +++ b/matita/matita/contribs/lambdadelta/apps_2/examples/ex_cpr_omega.ma @@ -34,7 +34,7 @@ lemma Delta_lifts (f) (s): ⇧*[f] (Delta s) ≘ (Delta s). (* Basic inversion properties ***********************************************) lemma cpr_inv_Delta1_body_sn (h) (G) (L) (s): - ∀X. ⦃G,L.ⓛ⋆s⦄ ⊢ ⓐ#O.#O ➡[h] X → ⓐ#O.#O = X. + ∀X. ❪G,L.ⓛ⋆s❫ ⊢ ⓐ#O.#O ➡[h] X → ⓐ#O.#O = X. #h #G #L #s #X #H lapply (cpm_inv_appl1 … H) -H * * [ #W2 #T2 #HW2 #HT2 #H destruct @@ -51,7 +51,7 @@ lapply (cpm_inv_appl1 … H) -H * * qed-. lemma cpr_inv_Delta_sn (h) (G) (L) (s): - ∀X. ⦃G,L⦄ ⊢ Delta s ➡[h] X → Delta s = X. + ∀X. ❪G,L❫ ⊢ Delta s ➡[h] X → Delta s = X. #h #G #L #s #X #H elim (cpm_inv_abst1 … H) -H #X1 #X2 #H1 #H2 #H destruct lapply (cpr_inv_sort1 … H1) -H1 #H destruct @@ -60,19 +60,19 @@ qed-. (* Main properties **********************************************************) -theorem cpr_Omega_12 (h) (G) (L) (s): ⦃G,L⦄ ⊢ Omega1 s ➡[h] Omega2 s. +theorem cpr_Omega_12 (h) (G) (L) (s): ❪G,L❫ ⊢ Omega1 s ➡[h] Omega2 s. /2 width=1 by cpm_beta/ qed. -theorem cpr_Omega_23 (h) (G) (L) (s): ⦃G,L⦄ ⊢ Omega2 s ➡[h] Omega3 s. +theorem cpr_Omega_23 (h) (G) (L) (s): ❪G,L❫ ⊢ Omega2 s ➡[h] Omega3 s. /5 width=3 by cpm_eps, cpm_appl, cpm_bind, cpm_delta, Delta_lifts/ qed. -theorem cpr_Omega_31 (h) (G) (L) (s): ⦃G,L⦄ ⊢ Omega3 s ➡[h] Omega1 s. +theorem cpr_Omega_31 (h) (G) (L) (s): ❪G,L❫ ⊢ Omega3 s ➡[h] Omega1 s. /4 width=3 by cpm_zeta, Delta_lifts, lifts_flat/ qed. (* Main inversion properties ************************************************) theorem cpr_inv_Omega1_sn (h) (G) (L) (s): - ∀X. ⦃G,L⦄ ⊢ Omega1 s ➡[h] X → + ∀X. ❪G,L❫ ⊢ Omega1 s ➡[h] X → ∨∨ Omega1 s = X | Omega2 s = X. #h #G #L #s #X #H elim (cpm_inv_appl1 … H) -H * [ #W2 #T2 #HW2 #HT2 #H destruct @@ -87,7 +87,7 @@ theorem cpr_inv_Omega1_sn (h) (G) (L) (s): ] qed-. -theorem cpr_Omega_21_false (h) (G) (L) (s): ⦃G,L⦄ ⊢ Omega2 s ➡[h] Omega1 s → ⊥. +theorem cpr_Omega_21_false (h) (G) (L) (s): ❪G,L❫ ⊢ Omega2 s ➡[h] Omega1 s → ⊥. #h #G #L #s #H elim (cpm_inv_bind1 … H) -H * [ #W #T #_ #_ whd in ⊢ (??%?→?); #H destruct | #X #H #_ #_ #_