X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_transition%2Fcpg.ma;h=e322f490f83aae1664fa7b5a60298c83daf37afd;hb=89ea663d91904f483f8248cfaeaed5eda8715da2;hp=fd44b81fd8816cbf44f0e1b11cdc01e13cbb703e;hpb=9a6cf8c3b53fe33515acd1aef8e7c7a10d71ae71;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg.ma index fd44b81fd..e322f490f 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg.ma @@ -12,6 +12,7 @@ (* *) (**************************************************************************) +include "ground_2/steps/rtc_max.ma". include "ground_2/steps/rtc_plus.ma". include "basic_2/notation/relations/predty_6.ma". include "basic_2/grammar/lenv.ma". @@ -33,21 +34,21 @@ inductive cpg (h): rtc → relation4 genv lenv term term ≝ ⬆*[1] T ≡ U → cpg h c G (L.ⓑ{I}V) (#⫯i) U | cpg_bind : ∀cV,cT,p,I,G,L,V1,V2,T1,T2. cpg h cV G L V1 V2 → cpg h cT G (L.ⓑ{I}V1) T1 T2 → - cpg h ((↓cV)+cT) G L (ⓑ{p,I}V1.T1) (ⓑ{p,I}V2.T2) + cpg h ((↓cV)∨cT) G L (ⓑ{p,I}V1.T1) (ⓑ{p,I}V2.T2) | cpg_flat : ∀cV,cT,I,G,L,V1,V2,T1,T2. cpg h cV G L V1 V2 → cpg h cT G L T1 T2 → - cpg h ((↓cV)+cT) G L (ⓕ{I}V1.T1) (ⓕ{I}V2.T2) + cpg h ((↓cV)∨cT) G L (ⓕ{I}V1.T1) (ⓕ{I}V2.T2) | cpg_zeta : ∀c,G,L,V,T1,T,T2. cpg h c G (L.ⓓV) T1 T → ⬆*[1] T2 ≡ T → cpg h (c+𝟙𝟘) G L (+ⓓV.T1) T2 | cpg_eps : ∀c,G,L,V,T1,T2. cpg h c G L T1 T2 → cpg h (c+𝟙𝟘) G L (ⓝV.T1) T2 | cpg_ee : ∀c,G,L,V1,V2,T. cpg h c G L V1 V2 → cpg h (c+𝟘𝟙) G L (ⓝV1.T) V2 | cpg_beta : ∀cV,cW,cT,p,G,L,V1,V2,W1,W2,T1,T2. cpg h cV G L V1 V2 → cpg h cW G L W1 W2 → cpg h cT G (L.ⓛW1) T1 T2 → - cpg h ((↓cV)+(↓cW)+cT+𝟙𝟘) G L (ⓐV1.ⓛ{p}W1.T1) (ⓓ{p}ⓝW2.V2.T2) + cpg h (((↓cV)∨(↓cW)∨cT)+𝟙𝟘) G L (ⓐV1.ⓛ{p}W1.T1) (ⓓ{p}ⓝW2.V2.T2) | cpg_theta: ∀cV,cW,cT,p,G,L,V1,V,V2,W1,W2,T1,T2. cpg h cV G L V1 V → ⬆*[1] V ≡ V2 → cpg h cW G L W1 W2 → cpg h cT G (L.ⓓW1) T1 T2 → - cpg h ((↓cV)+(↓cW)+cT+𝟙𝟘) G L (ⓐV1.ⓓ{p}W1.T1) (ⓓ{p}W2.ⓐV2.T2) + cpg h (((↓cV)∨(↓cW)∨cT)+𝟙𝟘) G L (ⓐV1.ⓓ{p}W1.T1) (ⓓ{p}W2.ⓐV2.T2) . interpretation @@ -151,7 +152,7 @@ qed-. fact cpg_inv_bind1_aux: ∀c,h,G,L,U,U2. ⦃G, L⦄ ⊢ U ⬈[c, h] U2 → ∀p,J,V1,U1. U = ⓑ{p,J}V1.U1 → ( ∃∃cV,cT,V2,T2. ⦃G, L⦄ ⊢ V1 ⬈[cV, h] V2 & ⦃G, L.ⓑ{J}V1⦄ ⊢ U1 ⬈[cT, h] T2 & - U2 = ⓑ{p,J}V2.T2 & c = (↓cV)+cT + U2 = ⓑ{p,J}V2.T2 & c = ((↓cV)∨cT) ) ∨ ∃∃cT,T. ⦃G, L.ⓓV1⦄ ⊢ U1 ⬈[cT, h] T & ⬆*[1] U2 ≡ T & p = true & J = Abbr & c = cT+𝟙𝟘. @@ -173,7 +174,7 @@ qed-. lemma cpg_inv_bind1: ∀c,h,p,I,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓑ{p,I}V1.T1 ⬈[c, h] U2 → ( ∃∃cV,cT,V2,T2. ⦃G, L⦄ ⊢ V1 ⬈[cV, h] V2 & ⦃G, L.ⓑ{I}V1⦄ ⊢ T1 ⬈[cT, h] T2 & - U2 = ⓑ{p,I}V2.T2 & c = (↓cV)+cT + U2 = ⓑ{p,I}V2.T2 & c = ((↓cV)∨cT) ) ∨ ∃∃cT,T. ⦃G, L.ⓓV1⦄ ⊢ T1 ⬈[cT, h] T & ⬆*[1] U2 ≡ T & p = true & I = Abbr & c = cT+𝟙𝟘. @@ -181,7 +182,7 @@ lemma cpg_inv_bind1: ∀c,h,p,I,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓑ{p,I}V1.T1 ⬈[c lemma cpg_inv_abbr1: ∀c,h,p,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓓ{p}V1.T1 ⬈[c, h] U2 → ( ∃∃cV,cT,V2,T2. ⦃G, L⦄ ⊢ V1 ⬈[cV, h] V2 & ⦃G, L.ⓓV1⦄ ⊢ T1 ⬈[cT, h] T2 & - U2 = ⓓ{p}V2.T2 & c = (↓cV)+cT + U2 = ⓓ{p}V2.T2 & c = ((↓cV)∨cT) ) ∨ ∃∃cT,T. ⦃G, L.ⓓV1⦄ ⊢ T1 ⬈[cT, h] T & ⬆*[1] U2 ≡ T & p = true & c = cT+𝟙𝟘. @@ -191,7 +192,7 @@ qed-. lemma cpg_inv_abst1: ∀c,h,p,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓛ{p}V1.T1 ⬈[c, h] U2 → ∃∃cV,cT,V2,T2. ⦃G, L⦄ ⊢ V1 ⬈[cV, h] V2 & ⦃G, L.ⓛV1⦄ ⊢ T1 ⬈[cT, h] T2 & - U2 = ⓛ{p}V2.T2 & c = (↓cV)+cT. + U2 = ⓛ{p}V2.T2 & c = ((↓cV)∨cT). #c #h #p #G #L #V1 #T1 #U2 #H elim (cpg_inv_bind1 … H) -H * [ /3 width=8 by ex4_4_intro/ | #c #T #_ #_ #_ #H destruct @@ -201,13 +202,13 @@ qed-. fact cpg_inv_flat1_aux: ∀c,h,G,L,U,U2. ⦃G, L⦄ ⊢ U ⬈[c, h] U2 → ∀J,V1,U1. U = ⓕ{J}V1.U1 → ∨∨ ∃∃cV,cT,V2,T2. ⦃G, L⦄ ⊢ V1 ⬈[cV, h] V2 & ⦃G, L⦄ ⊢ U1 ⬈[cT, h] T2 & - U2 = ⓕ{J}V2.T2 & c = (↓cV)+cT + U2 = ⓕ{J}V2.T2 & c = ((↓cV)∨cT) | ∃∃cT. ⦃G, L⦄ ⊢ U1 ⬈[cT, h] U2 & J = Cast & c = cT+𝟙𝟘 | ∃∃cV. ⦃G, L⦄ ⊢ V1 ⬈[cV, h] U2 & J = Cast & c = cV+𝟘𝟙 | ∃∃cV,cW,cT,p,V2,W1,W2,T1,T2. ⦃G, L⦄ ⊢ V1 ⬈[cV, h] V2 & ⦃G, L⦄ ⊢ W1 ⬈[cW, h] W2 & ⦃G, L.ⓛW1⦄ ⊢ T1 ⬈[cT, h] T2 & - J = Appl & U1 = ⓛ{p}W1.T1 & U2 = ⓓ{p}ⓝW2.V2.T2 & c = (↓cV)+(↓cW)+cT+𝟙𝟘 + J = Appl & U1 = ⓛ{p}W1.T1 & U2 = ⓓ{p}ⓝW2.V2.T2 & c = ((↓cV)∨(↓cW)∨cT)+𝟙𝟘 | ∃∃cV,cW,cT,p,V,V2,W1,W2,T1,T2. ⦃G, L⦄ ⊢ V1 ⬈[cV, h] V & ⬆*[1] V ≡ V2 & ⦃G, L⦄ ⊢ W1 ⬈[cW, h] W2 & ⦃G, L.ⓓW1⦄ ⊢ T1 ⬈[cT, h] T2 & - J = Appl & U1 = ⓓ{p}W1.T1 & U2 = ⓓ{p}W2.ⓐV2.T2 & c = (↓cV)+(↓cW)+cT+𝟙𝟘. + J = Appl & U1 = ⓓ{p}W1.T1 & U2 = ⓓ{p}W2.ⓐV2.T2 & c = ((↓cV)∨(↓cW)∨cT)+𝟙𝟘. #c #h #G #L #U #U2 * -c -G -L -U -U2 [ #I #G #L #J #W #U1 #H destruct | #G #L #s #J #W #U1 #H destruct @@ -226,22 +227,22 @@ qed-. lemma cpg_inv_flat1: ∀c,h,I,G,L,V1,U1,U2. ⦃G, L⦄ ⊢ ⓕ{I}V1.U1 ⬈[c, h] U2 → ∨∨ ∃∃cV,cT,V2,T2. ⦃G, L⦄ ⊢ V1 ⬈[cV, h] V2 & ⦃G, L⦄ ⊢ U1 ⬈[cT, h] T2 & - U2 = ⓕ{I}V2.T2 & c = (↓cV)+cT + U2 = ⓕ{I}V2.T2 & c = ((↓cV)∨cT) | ∃∃cT. ⦃G, L⦄ ⊢ U1 ⬈[cT, h] U2 & I = Cast & c = cT+𝟙𝟘 | ∃∃cV. ⦃G, L⦄ ⊢ V1 ⬈[cV, h] U2 & I = Cast & c = cV+𝟘𝟙 | ∃∃cV,cW,cT,p,V2,W1,W2,T1,T2. ⦃G, L⦄ ⊢ V1 ⬈[cV, h] V2 & ⦃G, L⦄ ⊢ W1 ⬈[cW, h] W2 & ⦃G, L.ⓛW1⦄ ⊢ T1 ⬈[cT, h] T2 & - I = Appl & U1 = ⓛ{p}W1.T1 & U2 = ⓓ{p}ⓝW2.V2.T2 & c = (↓cV)+(↓cW)+cT+𝟙𝟘 + I = Appl & U1 = ⓛ{p}W1.T1 & U2 = ⓓ{p}ⓝW2.V2.T2 & c = ((↓cV)∨(↓cW)∨cT)+𝟙𝟘 | ∃∃cV,cW,cT,p,V,V2,W1,W2,T1,T2. ⦃G, L⦄ ⊢ V1 ⬈[cV, h] V & ⬆*[1] V ≡ V2 & ⦃G, L⦄ ⊢ W1 ⬈[cW, h] W2 & ⦃G, L.ⓓW1⦄ ⊢ T1 ⬈[cT, h] T2 & - I = Appl & U1 = ⓓ{p}W1.T1 & U2 = ⓓ{p}W2.ⓐV2.T2 & c = (↓cV)+(↓cW)+cT+𝟙𝟘. + I = Appl & U1 = ⓓ{p}W1.T1 & U2 = ⓓ{p}W2.ⓐV2.T2 & c = ((↓cV)∨(↓cW)∨cT)+𝟙𝟘. /2 width=3 by cpg_inv_flat1_aux/ qed-. lemma cpg_inv_appl1: ∀c,h,G,L,V1,U1,U2. ⦃G, L⦄ ⊢ ⓐV1.U1 ⬈[c, h] U2 → ∨∨ ∃∃cV,cT,V2,T2. ⦃G, L⦄ ⊢ V1 ⬈[cV, h] V2 & ⦃G, L⦄ ⊢ U1 ⬈[cT, h] T2 & - U2 = ⓐV2.T2 & c = (↓cV)+cT + U2 = ⓐV2.T2 & c = ((↓cV)∨cT) | ∃∃cV,cW,cT,p,V2,W1,W2,T1,T2. ⦃G, L⦄ ⊢ V1 ⬈[cV, h] V2 & ⦃G, L⦄ ⊢ W1 ⬈[cW, h] W2 & ⦃G, L.ⓛW1⦄ ⊢ T1 ⬈[cT, h] T2 & - U1 = ⓛ{p}W1.T1 & U2 = ⓓ{p}ⓝW2.V2.T2 & c = (↓cV)+(↓cW)+cT+𝟙𝟘 + U1 = ⓛ{p}W1.T1 & U2 = ⓓ{p}ⓝW2.V2.T2 & c = ((↓cV)∨(↓cW)∨cT)+𝟙𝟘 | ∃∃cV,cW,cT,p,V,V2,W1,W2,T1,T2. ⦃G, L⦄ ⊢ V1 ⬈[cV, h] V & ⬆*[1] V ≡ V2 & ⦃G, L⦄ ⊢ W1 ⬈[cW, h] W2 & ⦃G, L.ⓓW1⦄ ⊢ T1 ⬈[cT, h] T2 & - U1 = ⓓ{p}W1.T1 & U2 = ⓓ{p}W2.ⓐV2.T2 & c = (↓cV)+(↓cW)+cT+𝟙𝟘. + U1 = ⓓ{p}W1.T1 & U2 = ⓓ{p}W2.ⓐV2.T2 & c = ((↓cV)∨(↓cW)∨cT)+𝟙𝟘. #c #h #G #L #V1 #U1 #U2 #H elim (cpg_inv_flat1 … H) -H * [ /3 width=8 by or3_intro0, ex4_4_intro/ |2,3: #c #_ #H destruct @@ -252,7 +253,7 @@ qed-. lemma cpg_inv_cast1: ∀c,h,G,L,V1,U1,U2. ⦃G, L⦄ ⊢ ⓝV1.U1 ⬈[c, h] U2 → ∨∨ ∃∃cV,cT,V2,T2. ⦃G, L⦄ ⊢ V1 ⬈[cV, h] V2 & ⦃G, L⦄ ⊢ U1 ⬈[cT, h] T2 & - U2 = ⓝV2.T2 & c = (↓cV)+cT + U2 = ⓝV2.T2 & c = ((↓cV)∨cT) | ∃∃cT. ⦃G, L⦄ ⊢ U1 ⬈[cT, h] U2 & c = cT+𝟙𝟘 | ∃∃cV. ⦃G, L⦄ ⊢ V1 ⬈[cV, h] U2 & c = cV+𝟘𝟙. #c #h #G #L #V1 #U1 #U2 #H elim (cpg_inv_flat1 … H) -H *