[ /2 width=3/
| #T1 #T3 #T #des #d #e #HT13 #_ #IHT13 #T2 #HT2
elim (IHT13 … HT2) -T #T #HT3 #HT2
- elim (lift_trans_le … HT13 … HT3 ?) -T3 // /3 width=5/
+ elim (lift_trans_le … HT13 … HT3) -T3 // /3 width=5/
]
qed-.
>(lifts_inv_nil … H) -T1 /2 width=3/
| #d #e #des #IHdes #i #i0 #H1 #des0 #H2 #T1 #T0 #HT10 #T2 #HT02
elim (at_inv_cons … H1) -H1 * #Hid #Hi0
- [ elim (minuss_inv_cons1_lt … H2 ?) -H2 [2: /2 width=1/ ] #des1 #Hdes1 <minus_le_minus_minus_comm // <minus_plus_m_m #H
+ [ elim (minuss_inv_cons1_lt … H2) -H2 [2: /2 width=1/ ] #des1 #Hdes1 <minus_le_minus_minus_comm // <minus_plus_m_m #H
elim (pluss_inv_cons2 … H) -H #des2 #H1 #H2 destruct
elim (lifts_inv_cons … HT10) -HT10 #T >minus_plus #HT1 #HT0
elim (IHdes … Hi0 … Hdes1 … HT0 … HT02) -IHdes -Hi0 -Hdes1 -T0 #T0 #HT0 #HT02
- elim (lift_trans_le … HT1 … HT0 ?) -T /2 width=1/ #T #HT1 <plus_minus_m_m /2 width=1/ /3 width=5/
+ elim (lift_trans_le … HT1 … HT0) -T /2 width=1/ #T #HT1 <plus_minus_m_m /2 width=1/ /3 width=5/
| >commutative_plus in Hi0; #Hi0
lapply (minuss_inv_cons1_ge … H2 ?) -H2 [ /2 width=1/ ] <associative_plus #Hdes0
elim (IHdes … Hi0 … Hdes0 … HT10 … HT02) -IHdes -Hi0 -Hdes0 -T0 #T0 #HT0 #HT02
- elim (lift_split … HT0 d (i+1) ? ? ?) -HT0 /2 width=1/ /3 width=5/
+ elim (lift_split … HT0 d (i+1)) -HT0 /2 width=1/ /3 width=5/
]
]
qed-.