(* *)
(**************************************************************************)
-include "ground_2/relocation/rtmap_basic.ma".
+include "ground/relocation/rtmap_basic.ma".
include "static_2/relocation/lifts.ma".
include "apps_2/models/veq.ma".
(* Forward lemmas with generic relocation ***********************************)
-fact lifts_fwd_vlift_aux (M): is_model M → is_extensional M →
- â\88\80f,T1,T2. â¬\86*[f] T1 â\89\98 T2 â\86\92 â\88\80m. ð\9d\90\81â\9d´m,1â\9dµ = f →
- ∀gv,lv,d. ⟦T1⟧[gv, lv] ≗{M} ⟦T2⟧[gv, ⫯[m←d]lv].
+fact lifts_fwd_vpush_aux (M): is_model M → is_extensional M →
+ â\88\80f,T1,T2. â\87§*[f] T1 â\89\98 T2 â\86\92 â\88\80m. ð\9d\90\9bâ\9d¨m,1â\9d© = f →
+ ∀gv,lv,d. ⟦T1⟧[gv,lv] ≗{M} ⟦T2⟧[gv,⫯[m←d]lv].
#M #H1M #H2M #f #T1 #T2 #H elim H -f -T1 -T2
[ #f #s #m #Hf #gv #lv #d
@(mq … H1M) [4,5: /3 width=2 by seq_sym, ms/ |1,2: skip ]
@(mq … H1M) [4,5: /3 width=2 by seq_sym, ml/ |1,2: skip ]
elim (lt_or_ge i1 m) #Hi1
[ lapply (at_basic_inv_lt … Hi12) -Hi12 // #H destruct
- >vlift_lt /2 width=1 by mr/
+ >vpush_lt /2 width=1 by mr/
| lapply (at_basic_inv_ge … Hi12) -Hi12 // #H destruct
- >vlift_gt /2 width=1 by mr, le_S_S/
+ >vpush_gt /2 width=1 by mr, le_S_S/
]
| #f #l #m #Hf #gv #lv #d
@(mq … H1M) [4,5: /3 width=2 by seq_sym, mg/ |1,2: skip ]
/2 width=1 by mr/
| #f #p * #V1 #V2 #T1 #T2 #_ #_ #IHV #IHT #m #Hm #gv #lv #d destruct
[ @(mq … H1M) [4,5: /3 width=2 by seq_sym, md/ |1,2: skip ]
+ @mc [3:|*: /2 width=1 by/ ]
@(seq_trans … H1M)
[3: @ti_comp // | skip ]
[1,2: /2 width=2 by veq_refl/ ]
- [2: @(vlift_comp … H1M) | skip ]
+ [2: @(vpush_comp … H1M) | skip ]
[1,2: /2 width=2 by/ |3,4: /2 width=2 by veq_refl/ ] -IHV
@(seq_trans … H1M)
[3: @ti_comp // | skip ]
[1,2: /2 width=2 by veq_refl/ ]
- [2: @veq_sym // @vlift_swap // | skip ]
+ [2: @veq_sym // @vpush_swap // | skip ]
/2 width=1 by/
| @mx // [ /2 width=1 by/ ] -IHV #d0
@(seq_trans … H1M)
[3: @ti_comp // | skip ]
[1,2: /2 width=2 by veq_refl/ ]
- [2: @veq_sym // @vlift_swap // | skip ]
+ [2: @veq_sym // @vpush_swap // | skip ]
/2 width=1 by/
]
| #f * #V1 #v2 #T1 #T2 #_ #_ #IHV #IHT #m #Hm #gv #lv #d
]
qed-.
-lemma lifts_SO_fwd_vlift (M) (gv): is_model M → is_extensional M →
- â\88\80T1,T2. â¬\86*[1] T1 ≘ T2 →
- ∀lv,d. ⟦T1⟧[gv, lv] ≗{M} ⟦T2⟧[gv, ⫯[0←d]lv].
-/2 width=3 by lifts_fwd_vlift_aux/ qed-.
+lemma lifts_SO_fwd_vpush (M) (gv): is_model M → is_extensional M →
+ â\88\80T1,T2. â\87§[1] T1 ≘ T2 →
+ ∀lv,d. ⟦T1⟧[gv,lv] ≗{M} ⟦T2⟧[gv,⫯[0←d]lv].
+/2 width=3 by lifts_fwd_vpush_aux/ qed-.