(* Basic_2A1: uses: fpb_inv_fleq *)
lemma fpb_inv_ffdeq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ →
⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ → ⊥.
#h #o #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
[ #G2 #L2 #T2 #H12 #H elim (ffdeq_inv_gen_sn … H) -H
(* Basic_2A1: uses: fpb_inv_fleq *)
lemma fpb_inv_ffdeq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ →
⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ → ⊥.
#h #o #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
[ #G2 #L2 #T2 #H12 #H elim (ffdeq_inv_gen_sn … H) -H
| #T2 #_ #HnT #H elim (ffdeq_inv_gen_sn … H) -H /2 width=1 by/
| #L2 #_ #HnL #H elim (ffdeq_inv_gen_sn … H) -H /2 width=1 by/
]
qed-.
| #T2 #_ #HnT #H elim (ffdeq_inv_gen_sn … H) -H /2 width=1 by/
| #L2 #_ #HnL #H elim (ffdeq_inv_gen_sn … H) -H /2 width=1 by/
]
qed-.