X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fetc%2Flleq%2Flleq_drop.etc;h=87ceaf096c88f8d3142b99993d02c237f8373b23;hb=6d1c6a2cfdd1909647db5648b9cd059c61b19b40;hp=aa4fa9e8c76ea747cc812bf4de5492dbfb8e2371;hpb=c0a8f89161e9887c38eb5cf701f0f0c05a0e527f;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/lleq/lleq_drop.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/lleq/lleq_drop.etc index aa4fa9e8c..87ceaf096 100644 --- a/matita/matita/contribs/lambdadelta/basic_2/etc/lleq/lleq_drop.etc +++ b/matita/matita/contribs/lambdadelta/basic_2/etc/lleq/lleq_drop.etc @@ -106,35 +106,6 @@ lemma lleq_fwd_bind_O_dx: ∀a,I,L1,L2,V,T. L1 ≡[ⓑ{a,I}V.T, 0] L2 → L1.ⓑ{I}V ≡[T, 0] L2.ⓑ{I}V. /2 width=2 by llpx_sn_fwd_bind_O_dx/ qed-. -(* Properties on relocation *************************************************) - -lemma lleq_lift_le: ∀K1,K2,T,lt. K1 ≡[T, lt] K2 → - ∀L1,L2,l,k. ⬇[Ⓕ, l, k] L1 ≡ K1 → ⬇[Ⓕ, l, k] L2 ≡ K2 → - ∀U. ⬆[l, k] T ≡ U → lt ≤ l → L1 ≡[U, lt] L2. -/3 width=10 by llpx_sn_lift_le, lift_mono/ qed-. - -lemma lleq_lift_ge: ∀K1,K2,T,lt. K1 ≡[T, lt] K2 → - ∀L1,L2,l,k. ⬇[Ⓕ, l, k] L1 ≡ K1 → ⬇[Ⓕ, l, k] L2 ≡ K2 → - ∀U. ⬆[l, k] T ≡ U → l ≤ lt → L1 ≡[U, lt+k] L2. -/2 width=9 by llpx_sn_lift_ge/ qed-. - -(* Inversion lemmas on relocation *******************************************) - -lemma lleq_inv_lift_le: ∀L1,L2,U,lt. L1 ≡[U, lt] L2 → - ∀K1,K2,l,k. ⬇[Ⓕ, l, k] L1 ≡ K1 → ⬇[Ⓕ, l, k] L2 ≡ K2 → - ∀T. ⬆[l, k] T ≡ U → lt ≤ l → K1 ≡[T, lt] K2. -/3 width=10 by llpx_sn_inv_lift_le, ex2_intro/ qed-. - -lemma lleq_inv_lift_be: ∀L1,L2,U,lt. L1 ≡[U, lt] L2 → - ∀K1,K2,l,k. ⬇[Ⓕ, l, k] L1 ≡ K1 → ⬇[Ⓕ, l, k] L2 ≡ K2 → - ∀T. ⬆[l, k] T ≡ U → l ≤ lt → lt ≤ l + k → K1 ≡[T, l] K2. -/2 width=11 by llpx_sn_inv_lift_be/ qed-. - -lemma lleq_inv_lift_ge: ∀L1,L2,U,lt. L1 ≡[U, lt] L2 → - ∀K1,K2,l,k. ⬇[Ⓕ, l, k] L1 ≡ K1 → ⬇[Ⓕ, l, k] L2 ≡ K2 → - ∀T. ⬆[l, k] T ≡ U → l + k ≤ lt → K1 ≡[T, lt-k] K2. -/2 width=9 by llpx_sn_inv_lift_ge/ qed-. - (* Inversion lemmas on negated lazy quivalence for local environments *******) lemma nlleq_inv_bind: ∀a,I,L1,L2,V,T,l. (L1 ≡[ⓑ{a,I}V.T, l] L2 → ⊥) →