X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_transition%2Fcpx.ma;h=ac024892379aa703d33377ffc012e9e834bb657b;hb=f694e3336cbdabdeefd86f85d827edfd26bf3464;hp=c4073314272cd31baa463371d7320bef43d1e2b9;hpb=b1c1894b6ee9a48c3b0bacd09be00938d8e20341;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx.ma index c40733142..ac0248923 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx.ma @@ -12,81 +12,81 @@ (* *) (**************************************************************************) -include "basic_2/notation/relations/pred_5.ma". +include "basic_2/notation/relations/predty_5.ma". include "basic_2/rt_transition/cpg.ma". -(* UNCOUNTED CONTEXT-SENSITIVE PARALLEL REDUCTION FOR TERMS *****************) +(* UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS *************) definition cpx (h): relation4 genv lenv term term ≝ - λG,L,T1,T2. ∃c. ⦃G, L⦄ ⊢ T1 ➡[c, h] T2. + λG,L,T1,T2. ∃c. ⦃G, L⦄ ⊢ T1 ⬈[c, h] T2. interpretation "uncounted context-sensitive parallel reduction (term)" - 'PRed h G L T1 T2 = (cpx h G L T1 T2). + 'PRedTy h G L T1 T2 = (cpx h G L T1 T2). (* Basic properties *********************************************************) -lemma cpx_atom: ∀h,I,G,L. ⦃G, L⦄ ⊢ ⓪{I} ➡[h] ⓪{I}. +lemma cpx_atom: ∀h,I,G,L. ⦃G, L⦄ ⊢ ⓪{I} ⬈[h] ⓪{I}. /2 width=2 by cpg_atom, ex_intro/ qed. (* Basic_2A1: was: cpx_st *) -lemma cpx_ess: ∀h,G,L,s. ⦃G, L⦄ ⊢ ⋆s ➡[h] ⋆(next h s). +lemma cpx_ess: ∀h,G,L,s. ⦃G, L⦄ ⊢ ⋆s ⬈[h] ⋆(next h s). /2 width=2 by cpg_ess, ex_intro/ qed. -lemma cpx_delta: ∀h,I,G,K,V1,V2,W2. ⦃G, K⦄ ⊢ V1 ➡[h] V2 → - ⬆*[1] V2 ≡ W2 → ⦃G, K.ⓑ{I}V1⦄ ⊢ #0 ➡[h] W2. +lemma cpx_delta: ∀h,I,G,K,V1,V2,W2. ⦃G, K⦄ ⊢ V1 ⬈[h] V2 → + ⬆*[1] V2 ≡ W2 → ⦃G, K.ⓑ{I}V1⦄ ⊢ #0 ⬈[h] W2. #h * #G #K #V1 #V2 #W2 * /3 width=4 by cpg_delta, cpg_ell, ex_intro/ qed. -lemma cpx_lref: ∀h,I,G,K,V,T,U,i. ⦃G, K⦄ ⊢ #i ➡[h] T → - ⬆*[1] T ≡ U → ⦃G, K.ⓑ{I}V⦄ ⊢ #⫯i ➡[h] U. +lemma cpx_lref: ∀h,I,G,K,V,T,U,i. ⦃G, K⦄ ⊢ #i ⬈[h] T → + ⬆*[1] T ≡ U → ⦃G, K.ⓑ{I}V⦄ ⊢ #⫯i ⬈[h] U. #h #I #G #K #V #T #U #i * /3 width=4 by cpg_lref, ex_intro/ qed. lemma cpx_bind: ∀h,p,I,G,L,V1,V2,T1,T2. - ⦃G, L⦄ ⊢ V1 ➡[h] V2 → ⦃G, L.ⓑ{I}V1⦄ ⊢ T1 ➡[h] T2 → - ⦃G, L⦄ ⊢ ⓑ{p,I}V1.T1 ➡[h] ⓑ{p,I}V2.T2. + ⦃G, L⦄ ⊢ V1 ⬈[h] V2 → ⦃G, L.ⓑ{I}V1⦄ ⊢ T1 ⬈[h] T2 → + ⦃G, L⦄ ⊢ ⓑ{p,I}V1.T1 ⬈[h] ⓑ{p,I}V2.T2. #h #p #I #G #L #V1 #V2 #T1 #T2 * #cV #HV12 * /3 width=2 by cpg_bind, ex_intro/ qed. lemma cpx_flat: ∀h,I,G,L,V1,V2,T1,T2. - ⦃G, L⦄ ⊢ V1 ➡[h] V2 → ⦃G, L⦄ ⊢ T1 ➡[h] T2 → - ⦃G, L⦄ ⊢ ⓕ{I}V1.T1 ➡[h] ⓕ{I}V2.T2. + ⦃G, L⦄ ⊢ V1 ⬈[h] V2 → ⦃G, L⦄ ⊢ T1 ⬈[h] T2 → + ⦃G, L⦄ ⊢ ⓕ{I}V1.T1 ⬈[h] ⓕ{I}V2.T2. #h #I #G #L #V1 #V2 #T1 #T2 * #cV #HV12 * /3 width=2 by cpg_flat, ex_intro/ qed. -lemma cpx_zeta: ∀h,G,L,V,T1,T,T2. ⦃G, L.ⓓV⦄ ⊢ T1 ➡[h] T → - ⬆*[1] T2 ≡ T → ⦃G, L⦄ ⊢ +ⓓV.T1 ➡[h] T2. +lemma cpx_zeta: ∀h,G,L,V,T1,T,T2. ⦃G, L.ⓓV⦄ ⊢ T1 ⬈[h] T → + ⬆*[1] T2 ≡ T → ⦃G, L⦄ ⊢ +ⓓV.T1 ⬈[h] T2. #h #G #L #V #T1 #T #T2 * /3 width=4 by cpg_zeta, ex_intro/ qed. -lemma cpx_eps: ∀h,G,L,V,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[h] T2 → ⦃G, L⦄ ⊢ ⓝV.T1 ➡[h] T2. +lemma cpx_eps: ∀h,G,L,V,T1,T2. ⦃G, L⦄ ⊢ T1 ⬈[h] T2 → ⦃G, L⦄ ⊢ ⓝV.T1 ⬈[h] T2. #h #G #L #V #T1 #T2 * /3 width=2 by cpg_eps, ex_intro/ qed. (* Basic_2A1: was: cpx_ct *) -lemma cpx_ee: ∀h,G,L,V1,V2,T. ⦃G, L⦄ ⊢ V1 ➡[h] V2 → ⦃G, L⦄ ⊢ ⓝV1.T ➡[h] V2. +lemma cpx_ee: ∀h,G,L,V1,V2,T. ⦃G, L⦄ ⊢ V1 ⬈[h] V2 → ⦃G, L⦄ ⊢ ⓝV1.T ⬈[h] V2. #h #G #L #V1 #V2 #T * /3 width=2 by cpg_ee, ex_intro/ qed. lemma cpx_beta: ∀h,p,G,L,V1,V2,W1,W2,T1,T2. - ⦃G, L⦄ ⊢ V1 ➡[h] V2 → ⦃G, L⦄ ⊢ W1 ➡[h] W2 → ⦃G, L.ⓛW1⦄ ⊢ T1 ➡[h] T2 → - ⦃G, L⦄ ⊢ ⓐV1.ⓛ{p}W1.T1 ➡[h] ⓓ{p}ⓝW2.V2.T2. + ⦃G, L⦄ ⊢ V1 ⬈[h] V2 → ⦃G, L⦄ ⊢ W1 ⬈[h] W2 → ⦃G, L.ⓛW1⦄ ⊢ T1 ⬈[h] T2 → + ⦃G, L⦄ ⊢ ⓐV1.ⓛ{p}W1.T1 ⬈[h] ⓓ{p}ⓝW2.V2.T2. #h #p #G #L #V1 #V2 #W1 #W2 #T1 #T2 * #cV #HV12 * #cW #HW12 * /3 width=2 by cpg_beta, ex_intro/ qed. lemma cpx_theta: ∀h,p,G,L,V1,V,V2,W1,W2,T1,T2. - ⦃G, L⦄ ⊢ V1 ➡[h] V → ⬆*[1] V ≡ V2 → ⦃G, L⦄ ⊢ W1 ➡[h] W2 → - ⦃G, L.ⓓW1⦄ ⊢ T1 ➡[h] T2 → - ⦃G, L⦄ ⊢ ⓐV1.ⓓ{p}W1.T1 ➡[h] ⓓ{p}W2.ⓐV2.T2. + ⦃G, L⦄ ⊢ V1 ⬈[h] V → ⬆*[1] V ≡ V2 → ⦃G, L⦄ ⊢ W1 ⬈[h] W2 → + ⦃G, L.ⓓW1⦄ ⊢ T1 ⬈[h] T2 → + ⦃G, L⦄ ⊢ ⓐV1.ⓓ{p}W1.T1 ⬈[h] ⓓ{p}W2.ⓐV2.T2. #h #p #G #L #V1 #V #V2 #W1 #W2 #T1 #T2 * #cV #HV1 #HV2 * #cW #HW12 * /3 width=4 by cpg_theta, ex_intro/ qed. @@ -94,119 +94,119 @@ qed. lemma cpx_refl: ∀h,G,L. reflexive … (cpx h G L). /2 width=2 by ex_intro/ qed. -lemma cpx_pair_sn: ∀h,I,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 → - ∀T. ⦃G, L⦄ ⊢ ②{I}V1.T ➡[h] ②{I}V2.T. +lemma cpx_pair_sn: ∀h,I,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ⬈[h] V2 → + ∀T. ⦃G, L⦄ ⊢ ②{I}V1.T ⬈[h] ②{I}V2.T. #h #I #G #L #V1 #V2 * /3 width=2 by cpg_pair_sn, ex_intro/ qed. (* Basic inversion lemmas ***************************************************) -lemma cpx_inv_atom1: ∀h,J,G,L,T2. ⦃G, L⦄ ⊢ ⓪{J} ➡[h] T2 → +lemma cpx_inv_atom1: ∀h,J,G,L,T2. ⦃G, L⦄ ⊢ ⓪{J} ⬈[h] T2 → ∨∨ T2 = ⓪{J} | ∃∃s. T2 = ⋆(next h s) & J = Sort s - | ∃∃I,K,V1,V2. ⦃G, K⦄ ⊢ V1 ➡[h] V2 & ⬆*[1] V2 ≡ T2 & + | ∃∃I,K,V1,V2. ⦃G, K⦄ ⊢ V1 ⬈[h] V2 & ⬆*[1] V2 ≡ T2 & L = K.ⓑ{I}V1 & J = LRef 0 - | ∃∃I,K,V,T,i. ⦃G, K⦄ ⊢ #i ➡[h] T & ⬆*[1] T ≡ T2 & + | ∃∃I,K,V,T,i. ⦃G, K⦄ ⊢ #i ⬈[h] T & ⬆*[1] T ≡ T2 & L = K.ⓑ{I}V & J = LRef (⫯i). #h #J #G #L #T2 * #c #H elim (cpg_inv_atom1 … H) -H * /4 width=9 by or4_intro0, or4_intro1, or4_intro2, or4_intro3, ex4_5_intro, ex4_4_intro, ex2_intro, ex_intro/ qed-. -lemma cpx_inv_sort1: ∀h,G,L,T2,s. ⦃G, L⦄ ⊢ ⋆s ➡[h] T2 → +lemma cpx_inv_sort1: ∀h,G,L,T2,s. ⦃G, L⦄ ⊢ ⋆s ⬈[h] T2 → T2 = ⋆s ∨ T2 = ⋆(next h s). #h #G #L #T2 #s * #c #H elim (cpg_inv_sort1 … H) -H * /2 width=1 by or_introl, or_intror/ qed-. -lemma cpx_inv_zero1: ∀h,G,L,T2. ⦃G, L⦄ ⊢ #0 ➡[h] T2 → +lemma cpx_inv_zero1: ∀h,G,L,T2. ⦃G, L⦄ ⊢ #0 ⬈[h] T2 → T2 = #0 ∨ - ∃∃I,K,V1,V2. ⦃G, K⦄ ⊢ V1 ➡[h] V2 & ⬆*[1] V2 ≡ T2 & + ∃∃I,K,V1,V2. ⦃G, K⦄ ⊢ V1 ⬈[h] V2 & ⬆*[1] V2 ≡ T2 & L = K.ⓑ{I}V1. #h #G #L #T2 * #c #H elim (cpg_inv_zero1 … H) -H * /4 width=7 by ex3_4_intro, ex_intro, or_introl, or_intror/ qed-. -lemma cpx_inv_lref1: ∀h,G,L,T2,i. ⦃G, L⦄ ⊢ #⫯i ➡[h] T2 → +lemma cpx_inv_lref1: ∀h,G,L,T2,i. ⦃G, L⦄ ⊢ #⫯i ⬈[h] T2 → T2 = #(⫯i) ∨ - ∃∃I,K,V,T. ⦃G, K⦄ ⊢ #i ➡[h] T & ⬆*[1] T ≡ T2 & L = K.ⓑ{I}V. + ∃∃I,K,V,T. ⦃G, K⦄ ⊢ #i ⬈[h] T & ⬆*[1] T ≡ T2 & L = K.ⓑ{I}V. #h #G #L #T2 #i * #c #H elim (cpg_inv_lref1 … H) -H * /4 width=7 by ex3_4_intro, ex_intro, or_introl, or_intror/ qed-. -lemma cpx_inv_gref1: ∀h,G,L,T2,l. ⦃G, L⦄ ⊢ §l ➡[h] T2 → T2 = §l. +lemma cpx_inv_gref1: ∀h,G,L,T2,l. ⦃G, L⦄ ⊢ §l ⬈[h] T2 → T2 = §l. #h #G #L #T2 #l * #c #H elim (cpg_inv_gref1 … H) -H // qed-. -lemma cpx_inv_bind1: ∀h,p,I,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓑ{p,I}V1.T1 ➡[h] U2 → ( - ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 & ⦃G, L.ⓑ{I}V1⦄ ⊢ T1 ➡[h] T2 & +lemma cpx_inv_bind1: ∀h,p,I,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓑ{p,I}V1.T1 ⬈[h] U2 → ( + ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ⬈[h] V2 & ⦃G, L.ⓑ{I}V1⦄ ⊢ T1 ⬈[h] T2 & U2 = ⓑ{p,I}V2.T2 ) ∨ - ∃∃T. ⦃G, L.ⓓV1⦄ ⊢ T1 ➡[h] T & ⬆*[1] U2 ≡ T & + ∃∃T. ⦃G, L.ⓓV1⦄ ⊢ T1 ⬈[h] T & ⬆*[1] U2 ≡ T & p = true & I = Abbr. #h #p #I #G #L #V1 #T1 #U2 * #c #H elim (cpg_inv_bind1 … H) -H * /4 width=5 by ex4_intro, ex3_2_intro, ex_intro, or_introl, or_intror/ qed-. -lemma cpx_inv_abbr1: ∀h,p,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓓ{p}V1.T1 ➡[h] U2 → ( - ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 & ⦃G, L.ⓓV1⦄ ⊢ T1 ➡[h] T2 & +lemma cpx_inv_abbr1: ∀h,p,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓓ{p}V1.T1 ⬈[h] U2 → ( + ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ⬈[h] V2 & ⦃G, L.ⓓV1⦄ ⊢ T1 ⬈[h] T2 & U2 = ⓓ{p}V2.T2 ) ∨ - ∃∃T. ⦃G, L.ⓓV1⦄ ⊢ T1 ➡[h] T & ⬆*[1] U2 ≡ T & p = true. + ∃∃T. ⦃G, L.ⓓV1⦄ ⊢ T1 ⬈[h] T & ⬆*[1] U2 ≡ T & p = true. #h #p #G #L #V1 #T1 #U2 * #c #H elim (cpg_inv_abbr1 … H) -H * /4 width=5 by ex3_2_intro, ex3_intro, ex_intro, or_introl, or_intror/ qed-. -lemma cpx_inv_abst1: ∀h,p,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓛ{p}V1.T1 ➡[h] U2 → - ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 & ⦃G, L.ⓛV1⦄ ⊢ T1 ➡[h] T2 & +lemma cpx_inv_abst1: ∀h,p,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓛ{p}V1.T1 ⬈[h] U2 → + ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ⬈[h] V2 & ⦃G, L.ⓛV1⦄ ⊢ T1 ⬈[h] T2 & U2 = ⓛ{p}V2.T2. #h #p #G #L #V1 #T1 #U2 * #c #H elim (cpg_inv_abst1 … H) -H /3 width=5 by ex3_2_intro, ex_intro/ qed-. -lemma cpx_inv_flat1: ∀h,I,G,L,V1,U1,U2. ⦃G, L⦄ ⊢ ⓕ{I}V1.U1 ➡[h] U2 → - ∨∨ ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 & ⦃G, L⦄ ⊢ U1 ➡[h] T2 & +lemma cpx_inv_flat1: ∀h,I,G,L,V1,U1,U2. ⦃G, L⦄ ⊢ ⓕ{I}V1.U1 ⬈[h] U2 → + ∨∨ ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ⬈[h] V2 & ⦃G, L⦄ ⊢ U1 ⬈[h] T2 & U2 = ⓕ{I}V2.T2 - | (⦃G, L⦄ ⊢ U1 ➡[h] U2 ∧ I = Cast) - | (⦃G, L⦄ ⊢ V1 ➡[h] U2 ∧ I = Cast) - | ∃∃p,V2,W1,W2,T1,T2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 & ⦃G, L⦄ ⊢ W1 ➡[h] W2 & - ⦃G, L.ⓛW1⦄ ⊢ T1 ➡[h] T2 & + | (⦃G, L⦄ ⊢ U1 ⬈[h] U2 ∧ I = Cast) + | (⦃G, L⦄ ⊢ V1 ⬈[h] U2 ∧ I = Cast) + | ∃∃p,V2,W1,W2,T1,T2. ⦃G, L⦄ ⊢ V1 ⬈[h] V2 & ⦃G, L⦄ ⊢ W1 ⬈[h] W2 & + ⦃G, L.ⓛW1⦄ ⊢ T1 ⬈[h] T2 & U1 = ⓛ{p}W1.T1 & U2 = ⓓ{p}ⓝW2.V2.T2 & I = Appl - | ∃∃p,V,V2,W1,W2,T1,T2. ⦃G, L⦄ ⊢ V1 ➡[h] V & ⬆*[1] V ≡ V2 & - ⦃G, L⦄ ⊢ W1 ➡[h] W2 & ⦃G, L.ⓓW1⦄ ⊢ T1 ➡[h] T2 & + | ∃∃p,V,V2,W1,W2,T1,T2. ⦃G, L⦄ ⊢ V1 ⬈[h] V & ⬆*[1] V ≡ V2 & + ⦃G, L⦄ ⊢ W1 ⬈[h] W2 & ⦃G, L.ⓓW1⦄ ⊢ T1 ⬈[h] T2 & U1 = ⓓ{p}W1.T1 & U2 = ⓓ{p}W2.ⓐV2.T2 & I = Appl. #h #I #G #L #V1 #U1 #U2 * #c #H elim (cpg_inv_flat1 … H) -H * /4 width=14 by or5_intro0, or5_intro1, or5_intro2, or5_intro3, or5_intro4, ex7_7_intro, ex6_6_intro, ex3_2_intro, ex_intro, conj/ qed-. -lemma cpx_inv_appl1: ∀h,G,L,V1,U1,U2. ⦃G, L⦄ ⊢ ⓐ V1.U1 ➡[h] U2 → - ∨∨ ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 & ⦃G, L⦄ ⊢ U1 ➡[h] T2 & +lemma cpx_inv_appl1: ∀h,G,L,V1,U1,U2. ⦃G, L⦄ ⊢ ⓐ V1.U1 ⬈[h] U2 → + ∨∨ ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ⬈[h] V2 & ⦃G, L⦄ ⊢ U1 ⬈[h] T2 & U2 = ⓐV2.T2 - | ∃∃p,V2,W1,W2,T1,T2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 & ⦃G, L⦄ ⊢ W1 ➡[h] W2 & - ⦃G, L.ⓛW1⦄ ⊢ T1 ➡[h] T2 & + | ∃∃p,V2,W1,W2,T1,T2. ⦃G, L⦄ ⊢ V1 ⬈[h] V2 & ⦃G, L⦄ ⊢ W1 ⬈[h] W2 & + ⦃G, L.ⓛW1⦄ ⊢ T1 ⬈[h] T2 & U1 = ⓛ{p}W1.T1 & U2 = ⓓ{p}ⓝW2.V2.T2 - | ∃∃p,V,V2,W1,W2,T1,T2. ⦃G, L⦄ ⊢ V1 ➡[h] V & ⬆*[1] V ≡ V2 & - ⦃G, L⦄ ⊢ W1 ➡[h] W2 & ⦃G, L.ⓓW1⦄ ⊢ T1 ➡[h] T2 & + | ∃∃p,V,V2,W1,W2,T1,T2. ⦃G, L⦄ ⊢ V1 ⬈[h] V & ⬆*[1] V ≡ V2 & + ⦃G, L⦄ ⊢ W1 ⬈[h] W2 & ⦃G, L.ⓓW1⦄ ⊢ T1 ⬈[h] T2 & U1 = ⓓ{p}W1.T1 & U2 = ⓓ{p}W2.ⓐV2.T2. #h #G #L #V1 #U1 #U2 * #c #H elim (cpg_inv_appl1 … H) -H * /4 width=13 by or3_intro0, or3_intro1, or3_intro2, ex6_7_intro, ex5_6_intro, ex3_2_intro, ex_intro/ qed-. -lemma cpx_inv_cast1: ∀h,G,L,V1,U1,U2. ⦃G, L⦄ ⊢ ⓝV1.U1 ➡[h] U2 → - ∨∨ ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 & ⦃G, L⦄ ⊢ U1 ➡[h] T2 & +lemma cpx_inv_cast1: ∀h,G,L,V1,U1,U2. ⦃G, L⦄ ⊢ ⓝV1.U1 ⬈[h] U2 → + ∨∨ ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ⬈[h] V2 & ⦃G, L⦄ ⊢ U1 ⬈[h] T2 & U2 = ⓝV2.T2 - | ⦃G, L⦄ ⊢ U1 ➡[h] U2 - | ⦃G, L⦄ ⊢ V1 ➡[h] U2. + | ⦃G, L⦄ ⊢ U1 ⬈[h] U2 + | ⦃G, L⦄ ⊢ V1 ⬈[h] U2. #h #G #L #V1 #U1 #U2 * #c #H elim (cpg_inv_cast1 … H) -H * /4 width=5 by or3_intro0, or3_intro1, or3_intro2, ex3_2_intro, ex_intro/ qed-. (* Basic forward lemmas *****************************************************) -lemma cpx_fwd_bind1_minus: ∀h,I,G,L,V1,T1,T. ⦃G, L⦄ ⊢ -ⓑ{I}V1.T1 ➡[h] T → ∀p. - ∃∃V2,T2. ⦃G, L⦄ ⊢ ⓑ{p,I}V1.T1 ➡[h] ⓑ{p,I}V2.T2 & +lemma cpx_fwd_bind1_minus: ∀h,I,G,L,V1,T1,T. ⦃G, L⦄ ⊢ -ⓑ{I}V1.T1 ⬈[h] T → ∀p. + ∃∃V2,T2. ⦃G, L⦄ ⊢ ⓑ{p,I}V1.T1 ⬈[h] ⓑ{p,I}V2.T2 & T = -ⓑ{I}V2.T2. #h #I #G #L #V1 #T1 #T * #c #H #p elim (cpg_fwd_bind1_minus … H p) -H /3 width=4 by ex2_2_intro, ex_intro/