X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_transition%2Frpx.ma;h=b3c8ba2fd43dec6fe786116bd215b73e09182263;hp=70351ad4f0bd7d1eeb8a5f2df770790fdf8dd497;hb=bd53c4e895203eb049e75434f638f26b5a161a2b;hpb=3b7b8afcb429a60d716d5226a5b6ab0d003228b1 diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/rpx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/rpx.ma index 70351ad4f..b3c8ba2fd 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/rpx.ma +++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/rpx.ma @@ -27,111 +27,111 @@ interpretation (* Basic properties ***********************************************************) -lemma rpx_atom: ∀h,I,G. ⦃G,⋆⦄ ⊢ ⬈[h,⓪{I}] ⋆. +lemma rpx_atom: ∀h,I,G. ❪G,⋆❫ ⊢ ⬈[h,⓪[I]] ⋆. /2 width=1 by rex_atom/ qed. lemma rpx_sort: ∀h,I1,I2,G,L1,L2,s. - ⦃G,L1⦄ ⊢ ⬈[h,⋆s] L2 → ⦃G,L1.ⓘ{I1}⦄ ⊢ ⬈[h,⋆s] L2.ⓘ{I2}. + ❪G,L1❫ ⊢ ⬈[h,⋆s] L2 → ❪G,L1.ⓘ[I1]❫ ⊢ ⬈[h,⋆s] L2.ⓘ[I2]. /2 width=1 by rex_sort/ qed. lemma rpx_pair: ∀h,I,G,L1,L2,V1,V2. - ⦃G,L1⦄ ⊢ ⬈[h,V1] L2 → ⦃G,L1⦄ ⊢ V1 ⬈[h] V2 → ⦃G,L1.ⓑ{I}V1⦄ ⊢ ⬈[h,#0] L2.ⓑ{I}V2. + ❪G,L1❫ ⊢ ⬈[h,V1] L2 → ❪G,L1❫ ⊢ V1 ⬈[h] V2 → ❪G,L1.ⓑ[I]V1❫ ⊢ ⬈[h,#0] L2.ⓑ[I]V2. /2 width=1 by rex_pair/ qed. lemma rpx_lref: ∀h,I1,I2,G,L1,L2,i. - ⦃G,L1⦄ ⊢ ⬈[h,#i] L2 → ⦃G,L1.ⓘ{I1}⦄ ⊢ ⬈[h,#↑i] L2.ⓘ{I2}. + ❪G,L1❫ ⊢ ⬈[h,#i] L2 → ❪G,L1.ⓘ[I1]❫ ⊢ ⬈[h,#↑i] L2.ⓘ[I2]. /2 width=1 by rex_lref/ qed. lemma rpx_gref: ∀h,I1,I2,G,L1,L2,l. - ⦃G,L1⦄ ⊢ ⬈[h,§l] L2 → ⦃G,L1.ⓘ{I1}⦄ ⊢ ⬈[h,§l] L2.ⓘ{I2}. + ❪G,L1❫ ⊢ ⬈[h,§l] L2 → ❪G,L1.ⓘ[I1]❫ ⊢ ⬈[h,§l] L2.ⓘ[I2]. /2 width=1 by rex_gref/ qed. lemma rpx_bind_repl_dx: ∀h,I,I1,G,L1,L2,T. - ⦃G,L1.ⓘ{I}⦄ ⊢ ⬈[h,T] L2.ⓘ{I1} → - ∀I2. ⦃G,L1⦄ ⊢ I ⬈[h] I2 → - ⦃G,L1.ⓘ{I}⦄ ⊢ ⬈[h,T] L2.ⓘ{I2}. + ❪G,L1.ⓘ[I]❫ ⊢ ⬈[h,T] L2.ⓘ[I1] → + ∀I2. ❪G,L1❫ ⊢ I ⬈[h] I2 → + ❪G,L1.ⓘ[I]❫ ⊢ ⬈[h,T] L2.ⓘ[I2]. /2 width=2 by rex_bind_repl_dx/ qed-. (* Basic inversion lemmas ***************************************************) -lemma rpx_inv_atom_sn: ∀h,G,Y2,T. ⦃G,⋆⦄ ⊢ ⬈[h,T] Y2 → Y2 = ⋆. +lemma rpx_inv_atom_sn: ∀h,G,Y2,T. ❪G,⋆❫ ⊢ ⬈[h,T] Y2 → Y2 = ⋆. /2 width=3 by rex_inv_atom_sn/ qed-. -lemma rpx_inv_atom_dx: ∀h,G,Y1,T. ⦃G,Y1⦄ ⊢ ⬈[h,T] ⋆ → Y1 = ⋆. +lemma rpx_inv_atom_dx: ∀h,G,Y1,T. ❪G,Y1❫ ⊢ ⬈[h,T] ⋆ → Y1 = ⋆. /2 width=3 by rex_inv_atom_dx/ qed-. -lemma rpx_inv_sort: ∀h,G,Y1,Y2,s. ⦃G,Y1⦄ ⊢ ⬈[h,⋆s] Y2 → +lemma rpx_inv_sort: ∀h,G,Y1,Y2,s. ❪G,Y1❫ ⊢ ⬈[h,⋆s] Y2 → ∨∨ Y1 = ⋆ ∧ Y2 = ⋆ - | ∃∃I1,I2,L1,L2. ⦃G,L1⦄ ⊢ ⬈[h,⋆s] L2 & - Y1 = L1.ⓘ{I1} & Y2 = L2.ⓘ{I2}. + | ∃∃I1,I2,L1,L2. ❪G,L1❫ ⊢ ⬈[h,⋆s] L2 & + Y1 = L1.ⓘ[I1] & Y2 = L2.ⓘ[I2]. /2 width=1 by rex_inv_sort/ qed-. -lemma rpx_inv_lref: ∀h,G,Y1,Y2,i. ⦃G,Y1⦄ ⊢ ⬈[h,#↑i] Y2 → +lemma rpx_inv_lref: ∀h,G,Y1,Y2,i. ❪G,Y1❫ ⊢ ⬈[h,#↑i] Y2 → ∨∨ Y1 = ⋆ ∧ Y2 = ⋆ - | ∃∃I1,I2,L1,L2. ⦃G,L1⦄ ⊢ ⬈[h,#i] L2 & - Y1 = L1.ⓘ{I1} & Y2 = L2.ⓘ{I2}. + | ∃∃I1,I2,L1,L2. ❪G,L1❫ ⊢ ⬈[h,#i] L2 & + Y1 = L1.ⓘ[I1] & Y2 = L2.ⓘ[I2]. /2 width=1 by rex_inv_lref/ qed-. -lemma rpx_inv_gref: ∀h,G,Y1,Y2,l. ⦃G,Y1⦄ ⊢ ⬈[h,§l] Y2 → +lemma rpx_inv_gref: ∀h,G,Y1,Y2,l. ❪G,Y1❫ ⊢ ⬈[h,§l] Y2 → ∨∨ Y1 = ⋆ ∧ Y2 = ⋆ - | ∃∃I1,I2,L1,L2. ⦃G,L1⦄ ⊢ ⬈[h,§l] L2 & - Y1 = L1.ⓘ{I1} & Y2 = L2.ⓘ{I2}. + | ∃∃I1,I2,L1,L2. ❪G,L1❫ ⊢ ⬈[h,§l] L2 & + Y1 = L1.ⓘ[I1] & Y2 = L2.ⓘ[I2]. /2 width=1 by rex_inv_gref/ qed-. -lemma rpx_inv_bind: ∀h,p,I,G,L1,L2,V,T. ⦃G,L1⦄ ⊢ ⬈[h,ⓑ{p,I}V.T] L2 → - ∧∧ ⦃G,L1⦄ ⊢ ⬈[h,V] L2 & ⦃G,L1.ⓑ{I}V⦄ ⊢ ⬈[h,T] L2.ⓑ{I}V. +lemma rpx_inv_bind: ∀h,p,I,G,L1,L2,V,T. ❪G,L1❫ ⊢ ⬈[h,ⓑ[p,I]V.T] L2 → + ∧∧ ❪G,L1❫ ⊢ ⬈[h,V] L2 & ❪G,L1.ⓑ[I]V❫ ⊢ ⬈[h,T] L2.ⓑ[I]V. /2 width=2 by rex_inv_bind/ qed-. -lemma rpx_inv_flat: ∀h,I,G,L1,L2,V,T. ⦃G,L1⦄ ⊢ ⬈[h,ⓕ{I}V.T] L2 → - ∧∧ ⦃G,L1⦄ ⊢ ⬈[h,V] L2 & ⦃G,L1⦄ ⊢ ⬈[h,T] L2. +lemma rpx_inv_flat: ∀h,I,G,L1,L2,V,T. ❪G,L1❫ ⊢ ⬈[h,ⓕ[I]V.T] L2 → + ∧∧ ❪G,L1❫ ⊢ ⬈[h,V] L2 & ❪G,L1❫ ⊢ ⬈[h,T] L2. /2 width=2 by rex_inv_flat/ qed-. (* Advanced inversion lemmas ************************************************) -lemma rpx_inv_sort_bind_sn: ∀h,I1,G,Y2,L1,s. ⦃G,L1.ⓘ{I1}⦄ ⊢ ⬈[h,⋆s] Y2 → - ∃∃I2,L2. ⦃G,L1⦄ ⊢ ⬈[h,⋆s] L2 & Y2 = L2.ⓘ{I2}. +lemma rpx_inv_sort_bind_sn: ∀h,I1,G,Y2,L1,s. ❪G,L1.ⓘ[I1]❫ ⊢ ⬈[h,⋆s] Y2 → + ∃∃I2,L2. ❪G,L1❫ ⊢ ⬈[h,⋆s] L2 & Y2 = L2.ⓘ[I2]. /2 width=2 by rex_inv_sort_bind_sn/ qed-. -lemma rpx_inv_sort_bind_dx: ∀h,I2,G,Y1,L2,s. ⦃G,Y1⦄ ⊢ ⬈[h,⋆s] L2.ⓘ{I2} → - ∃∃I1,L1. ⦃G,L1⦄ ⊢ ⬈[h,⋆s] L2 & Y1 = L1.ⓘ{I1}. +lemma rpx_inv_sort_bind_dx: ∀h,I2,G,Y1,L2,s. ❪G,Y1❫ ⊢ ⬈[h,⋆s] L2.ⓘ[I2] → + ∃∃I1,L1. ❪G,L1❫ ⊢ ⬈[h,⋆s] L2 & Y1 = L1.ⓘ[I1]. /2 width=2 by rex_inv_sort_bind_dx/ qed-. -lemma rpx_inv_zero_pair_sn: ∀h,I,G,Y2,L1,V1. ⦃G,L1.ⓑ{I}V1⦄ ⊢ ⬈[h,#0] Y2 → - ∃∃L2,V2. ⦃G,L1⦄ ⊢ ⬈[h,V1] L2 & ⦃G,L1⦄ ⊢ V1 ⬈[h] V2 & - Y2 = L2.ⓑ{I}V2. +lemma rpx_inv_zero_pair_sn: ∀h,I,G,Y2,L1,V1. ❪G,L1.ⓑ[I]V1❫ ⊢ ⬈[h,#0] Y2 → + ∃∃L2,V2. ❪G,L1❫ ⊢ ⬈[h,V1] L2 & ❪G,L1❫ ⊢ V1 ⬈[h] V2 & + Y2 = L2.ⓑ[I]V2. /2 width=1 by rex_inv_zero_pair_sn/ qed-. -lemma rpx_inv_zero_pair_dx: ∀h,I,G,Y1,L2,V2. ⦃G,Y1⦄ ⊢ ⬈[h,#0] L2.ⓑ{I}V2 → - ∃∃L1,V1. ⦃G,L1⦄ ⊢ ⬈[h,V1] L2 & ⦃G,L1⦄ ⊢ V1 ⬈[h] V2 & - Y1 = L1.ⓑ{I}V1. +lemma rpx_inv_zero_pair_dx: ∀h,I,G,Y1,L2,V2. ❪G,Y1❫ ⊢ ⬈[h,#0] L2.ⓑ[I]V2 → + ∃∃L1,V1. ❪G,L1❫ ⊢ ⬈[h,V1] L2 & ❪G,L1❫ ⊢ V1 ⬈[h] V2 & + Y1 = L1.ⓑ[I]V1. /2 width=1 by rex_inv_zero_pair_dx/ qed-. -lemma rpx_inv_lref_bind_sn: ∀h,I1,G,Y2,L1,i. ⦃G,L1.ⓘ{I1}⦄ ⊢ ⬈[h,#↑i] Y2 → - ∃∃I2,L2. ⦃G,L1⦄ ⊢ ⬈[h,#i] L2 & Y2 = L2.ⓘ{I2}. +lemma rpx_inv_lref_bind_sn: ∀h,I1,G,Y2,L1,i. ❪G,L1.ⓘ[I1]❫ ⊢ ⬈[h,#↑i] Y2 → + ∃∃I2,L2. ❪G,L1❫ ⊢ ⬈[h,#i] L2 & Y2 = L2.ⓘ[I2]. /2 width=2 by rex_inv_lref_bind_sn/ qed-. -lemma rpx_inv_lref_bind_dx: ∀h,I2,G,Y1,L2,i. ⦃G,Y1⦄ ⊢ ⬈[h,#↑i] L2.ⓘ{I2} → - ∃∃I1,L1. ⦃G,L1⦄ ⊢ ⬈[h,#i] L2 & Y1 = L1.ⓘ{I1}. +lemma rpx_inv_lref_bind_dx: ∀h,I2,G,Y1,L2,i. ❪G,Y1❫ ⊢ ⬈[h,#↑i] L2.ⓘ[I2] → + ∃∃I1,L1. ❪G,L1❫ ⊢ ⬈[h,#i] L2 & Y1 = L1.ⓘ[I1]. /2 width=2 by rex_inv_lref_bind_dx/ qed-. -lemma rpx_inv_gref_bind_sn: ∀h,I1,G,Y2,L1,l. ⦃G,L1.ⓘ{I1}⦄ ⊢ ⬈[h,§l] Y2 → - ∃∃I2,L2. ⦃G,L1⦄ ⊢ ⬈[h,§l] L2 & Y2 = L2.ⓘ{I2}. +lemma rpx_inv_gref_bind_sn: ∀h,I1,G,Y2,L1,l. ❪G,L1.ⓘ[I1]❫ ⊢ ⬈[h,§l] Y2 → + ∃∃I2,L2. ❪G,L1❫ ⊢ ⬈[h,§l] L2 & Y2 = L2.ⓘ[I2]. /2 width=2 by rex_inv_gref_bind_sn/ qed-. -lemma rpx_inv_gref_bind_dx: ∀h,I2,G,Y1,L2,l. ⦃G,Y1⦄ ⊢ ⬈[h,§l] L2.ⓘ{I2} → - ∃∃I1,L1. ⦃G,L1⦄ ⊢ ⬈[h,§l] L2 & Y1 = L1.ⓘ{I1}. +lemma rpx_inv_gref_bind_dx: ∀h,I2,G,Y1,L2,l. ❪G,Y1❫ ⊢ ⬈[h,§l] L2.ⓘ[I2] → + ∃∃I1,L1. ❪G,L1❫ ⊢ ⬈[h,§l] L2 & Y1 = L1.ⓘ[I1]. /2 width=2 by rex_inv_gref_bind_dx/ qed-. (* Basic forward lemmas *****************************************************) lemma rpx_fwd_pair_sn: ∀h,I,G,L1,L2,V,T. - ⦃G,L1⦄ ⊢ ⬈[h,②{I}V.T] L2 → ⦃G,L1⦄ ⊢ ⬈[h,V] L2. + ❪G,L1❫ ⊢ ⬈[h,②[I]V.T] L2 → ❪G,L1❫ ⊢ ⬈[h,V] L2. /2 width=3 by rex_fwd_pair_sn/ qed-. lemma rpx_fwd_bind_dx: ∀h,p,I,G,L1,L2,V,T. - ⦃G,L1⦄ ⊢ ⬈[h,ⓑ{p,I}V.T] L2 → ⦃G,L1.ⓑ{I}V⦄ ⊢ ⬈[h,T] L2.ⓑ{I}V. + ❪G,L1❫ ⊢ ⬈[h,ⓑ[p,I]V.T] L2 → ❪G,L1.ⓑ[I]V❫ ⊢ ⬈[h,T] L2.ⓑ[I]V. /2 width=2 by rex_fwd_bind_dx/ qed-. lemma rpx_fwd_flat_dx: ∀h,I,G,L1,L2,V,T. - ⦃G,L1⦄ ⊢ ⬈[h,ⓕ{I}V.T] L2 → ⦃G,L1⦄ ⊢ ⬈[h,T] L2. + ❪G,L1❫ ⊢ ⬈[h,ⓕ[I]V.T] L2 → ❪G,L1❫ ⊢ ⬈[h,T] L2. /2 width=3 by rex_fwd_flat_dx/ qed-.