X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fstatic_2%2Fstatic%2Freqx_reqx.ma;h=3d4c8921cbbf67888cbea2270a62ae38e950d4dc;hp=f7322ee5e7247b93902e70180166b6a33b981400;hb=bd53c4e895203eb049e75434f638f26b5a161a2b;hpb=3b7b8afcb429a60d716d5226a5b6ab0d003228b1 diff --git a/matita/matita/contribs/lambdadelta/static_2/static/reqx_reqx.ma b/matita/matita/contribs/lambdadelta/static_2/static/reqx_reqx.ma index f7322ee5e..3d4c8921c 100644 --- a/matita/matita/contribs/lambdadelta/static_2/static/reqx_reqx.ma +++ b/matita/matita/contribs/lambdadelta/static_2/static/reqx_reqx.ma @@ -32,17 +32,17 @@ lemma reqx_dec: ∀L1,L2. ∀T:term. Decidable (L1 ≛[T] L2). (* Basic_2A1: uses: lleq_bind lleq_bind_O *) theorem reqx_bind: ∀p,I,L1,L2,V1,V2,T. - L1 ≛[V1] L2 → L1.ⓑ{I}V1 ≛[T] L2.ⓑ{I}V2 → - L1 ≛[ⓑ{p,I}V1.T] L2. + L1 ≛[V1] L2 → L1.ⓑ[I]V1 ≛[T] L2.ⓑ[I]V2 → + L1 ≛[ⓑ[p,I]V1.T] L2. /2 width=2 by rex_bind/ qed. (* Basic_2A1: uses: lleq_flat *) theorem reqx_flat: ∀I,L1,L2,V,T. - L1 ≛[V] L2 → L1 ≛[T] L2 → L1 ≛[ⓕ{I}V.T] L2. + L1 ≛[V] L2 → L1 ≛[T] L2 → L1 ≛[ⓕ[I]V.T] L2. /2 width=1 by rex_flat/ qed. theorem reqx_bind_void: ∀p,I,L1,L2,V,T. - L1 ≛[V] L2 → L1.ⓧ ≛[T] L2.ⓧ → L1 ≛[ⓑ{p,I}V.T] L2. + L1 ≛[V] L2 → L1.ⓧ ≛[T] L2.ⓧ → L1 ≛[ⓑ[p,I]V.T] L2. /2 width=1 by rex_bind_void/ qed. (* Basic_2A1: uses: lleq_trans *) @@ -85,15 +85,15 @@ theorem rneqx_reqx_canc_dx: ∀L1,L. ∀T:term. (L1 ≛[T] L → ⊥) → (* Negated inversion lemmas *************************************************) (* Basic_2A1: uses: nlleq_inv_bind nlleq_inv_bind_O *) -lemma rneqx_inv_bind: ∀p,I,L1,L2,V,T. (L1 ≛[ⓑ{p,I}V.T] L2 → ⊥) → - (L1 ≛[V] L2 → ⊥) ∨ (L1.ⓑ{I}V ≛[T] L2.ⓑ{I}V → ⊥). +lemma rneqx_inv_bind: ∀p,I,L1,L2,V,T. (L1 ≛[ⓑ[p,I]V.T] L2 → ⊥) → + (L1 ≛[V] L2 → ⊥) ∨ (L1.ⓑ[I]V ≛[T] L2.ⓑ[I]V → ⊥). /3 width=2 by rnex_inv_bind, teqx_dec/ qed-. (* Basic_2A1: uses: nlleq_inv_flat *) -lemma rneqx_inv_flat: ∀I,L1,L2,V,T. (L1 ≛[ⓕ{I}V.T] L2 → ⊥) → +lemma rneqx_inv_flat: ∀I,L1,L2,V,T. (L1 ≛[ⓕ[I]V.T] L2 → ⊥) → (L1 ≛[V] L2 → ⊥) ∨ (L1 ≛[T] L2 → ⊥). /3 width=2 by rnex_inv_flat, teqx_dec/ qed-. -lemma rneqx_inv_bind_void: ∀p,I,L1,L2,V,T. (L1 ≛[ⓑ{p,I}V.T] L2 → ⊥) → +lemma rneqx_inv_bind_void: ∀p,I,L1,L2,V,T. (L1 ≛[ⓑ[p,I]V.T] L2 → ⊥) → (L1 ≛[V] L2 → ⊥) ∨ (L1.ⓧ ≛[T] L2.ⓧ → ⊥). /3 width=3 by rnex_inv_bind_void, teqx_dec/ qed-.