lemma lleq_inv_lift_be: ∀L1,L2,U,lt. L1 ≡[U, lt] L2 →
∀K1,K2,l,m. ⬇[Ⓕ, l, m] L1 ≡ K1 → ⬇[Ⓕ, l, m] L2 ≡ K2 →
- ∀T. ⬆[l, m] T ≡ U → l ≤ lt → lt ≤ yinj l + m → K1 ≡[T, l] K2.
+ ∀T. ⬆[l, m] T ≡ U → l ≤ lt → lt ≤ l + m → 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,m. ⬇[Ⓕ, l, m] L1 ≡ K1 → ⬇[Ⓕ, l, m] L2 ≡ K2 →
- ∀T. ⬆[l, m] T ≡ U → yinj l + m ≤ lt → K1 ≡[T, lt-m] K2.
+ ∀T. ⬆[l, m] T ≡ U → l + m ≤ lt → K1 ≡[T, lt-m] K2.
/2 width=9 by llpx_sn_inv_lift_ge/ qed-.
(* Inversion lemmas on negated lazy quivalence for local environments *******)