(* Forward lemmas with context-sensitive parallel reduction for terms *******)
lemma cpr_fwd_deq (h) (M): is_model M → is_extensional M →
- â\88\80G,L,T1,T2. â¦\83G, Lâ¦\84 â\8a¢ T1 â\9e¡[h] T2 â\86\92 â¦\83G, Lâ¦\84 ⊢ T1 ≗{M} T2.
+ â\88\80G,L,T1,T2. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡[h] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ T1 ≗{M} T2.
#h #M #H1M #H2M #G #L #T1 #T2 #H @(cpr_ind … H) -G -L -T1 -T2
[ /2 width=2 by deq_refl/
| #G #K #V1 #V2 #W2 #_ #IH #HVW2 #gv #v #H
| @(mq … H1M) [4,5: /3 width=2 by seq_sym, me/ |1,2: skip ]
/2 width=1 by/
]
-| #G #L #V #U1 #U2 #T2 #_ #IH #HTU2 #gv #lv #Hlv
+| #G #L #V #U1 #T1 #T2 #HTU1 #_ #IH #gv #lv #Hlv
@(mq … H1M)
[4: /3 width=2 by seq_sym, md/ | skip
|3: @(seq_trans … H1M) [2: @mz // | skip ]
- /3 width=1 by li_abbr/
- |2: skip ] -L -U1
- /3 width=1 by lifts_SO_fwd_vpush, seq_sym/
+ ] /3 width=3 by lifts_SO_fwd_vpush, seq_sym/
| #G #L #V #T1 #T2 #_ #IH #gv #lv #Hlv
@(seq_trans … H1M) [2: @(me … H1M) | skip ]
/2 width=1 by/