lemma veq_canc_dx (M): is_model M → right_cancellable … (veq M).
/3 width=3 by veq_trans, veq_sym/ qed-.
lemma veq_canc_dx (M): is_model M → right_cancellable … (veq M).
/3 width=3 by veq_trans, veq_sym/ qed-.
∀i1,i2. i1 ≤ i2 →
∀lv,d1,d2. ⫯[i1←d1] ⫯[i2←d2] lv ≗{M} ⫯[↑i2←d2] ⫯[i1←d1] lv.
#M #HM #i1 #i2 #Hi12 #lv #d1 #d2 #j
elim (lt_or_eq_or_gt j i1) #Hji1 destruct
[ lapply (lt_to_le_to_lt … Hji1 Hi12) #Hji2
∀i1,i2. i1 ≤ i2 →
∀lv,d1,d2. ⫯[i1←d1] ⫯[i2←d2] lv ≗{M} ⫯[↑i2←d2] ⫯[i1←d1] lv.
#M #HM #i1 #i2 #Hi12 #lv #d1 #d2 #j
elim (lt_or_eq_or_gt j i1) #Hji1 destruct
[ lapply (lt_to_le_to_lt … Hji1 Hi12) #Hji2
-| >vlift_gt // elim (lt_or_eq_or_gt (↓j) i2) #Hji2 destruct
- [ >vlift_lt // >vlift_lt /2 width=1 by lt_minus_to_plus/ >vlift_gt //
+| >vpush_gt // elim (lt_or_eq_or_gt (↓j) i2) #Hji2 destruct
+ [ >vpush_lt // >vpush_lt /2 width=1 by lt_minus_to_plus/ >vpush_gt //
-[ >vlift_lt // >vlift_lt //
-| >vlift_eq >vlift_eq //
-| >vlift_gt // >vlift_gt //
+[ >vpush_lt // >vpush_lt //
+| >vpush_eq >vpush_eq //
+| >vpush_gt // >vpush_gt //
lemma ti_comp (M): is_model M →
∀T,gv1,gv2. gv1 ≗ gv2 → ∀lv1,lv2. lv1 ≗ lv2 →
lemma ti_comp (M): is_model M →
∀T,gv1,gv2. gv1 ≗ gv2 → ∀lv1,lv2. lv1 ≗ lv2 →
#M #HM #T elim T -T * [||| #p * | * ]
[ /4 width=5 by seq_trans, seq_sym, ms/
| /4 width=5 by seq_sym, ml, mq/
| /4 width=3 by seq_trans, seq_sym, mg/
#M #HM #T elim T -T * [||| #p * | * ]
[ /4 width=5 by seq_trans, seq_sym, ms/
| /4 width=5 by seq_sym, ml, mq/
| /4 width=3 by seq_trans, seq_sym, mg/
-| /5 width=5 by vlift_comp, seq_sym, md, mq/
-| /5 width=1 by vlift_comp, mi, mr/
+| /6 width=5 by vpush_comp, seq_sym, md, mc, mq/
+| /5 width=1 by vpush_comp, mi, mr/
| /4 width=5 by seq_sym, ma, mp, mq/
| /4 width=5 by seq_sym, me, mq/
]
| /4 width=5 by seq_sym, ma, mp, mq/
| /4 width=5 by seq_sym, me, mq/
]