(* Note: this is used in the closure proof *)
lemma cpr_lpr_sta_fpbs: ∀h,g,G,L1,L2,T1,T2,U2,l2.
⦃G, L1⦄ ⊢ T1 ➡ T2 → ⦃G, L1⦄ ⊢ ➡ L2 →
⦃G, L2⦄ ⊢ T2 ▪[h, g] l2+1 → ⦃G, L2⦄ ⊢ T2 •*[h, 1] U2 →
⦃G, L1, T1⦄ ≥[h, g] ⦃G, L2, U2⦄.
(* Note: this is used in the closure proof *)
lemma cpr_lpr_sta_fpbs: ∀h,g,G,L1,L2,T1,T2,U2,l2.
⦃G, L1⦄ ⊢ T1 ➡ T2 → ⦃G, L1⦄ ⊢ ➡ L2 →
⦃G, L2⦄ ⊢ T2 ▪[h, g] l2+1 → ⦃G, L2⦄ ⊢ T2 •*[h, 1] U2 →
⦃G, L1, T1⦄ ≥[h, g] ⦃G, L2, U2⦄.