(* substitution *************************************************************)
-notation "hvbox( [ d , break e ] ↑ break T1 ≡ break T2 )"
+notation "hvbox( ↑ [ d , break e ] break T1 ≡ break T2 )"
non associative with precedence 45
for @{ 'RLift $T1 $d $e $T2 }.
-notation "hvbox( [ d , break e ] ← break (term 90 L) / break T1 ≡ break T2 )"
+notation "hvbox( ↓ [ d , break e ] break L1 ≡ break L2 )"
non associative with precedence 45
- for @{ 'RSubst $L $T1 $d $e $T2 }.
+ for @{ 'RSubst $L1 $d $e $L2 }.
-notation "hvbox( [ d , break e ] ↓ break L1 ≡ break L2 )"
+notation "hvbox( L ⊢ break ↓ [ d , break e ] break T1 ≡ break T2 )"
non associative with precedence 45
- for @{ 'RThin $L1 $d $e $L2 }.
+ for @{ 'RSubst $L $T1 $d $e $T2 }.
(* reduction ****************************************************************)
| subst_lref_lt: ∀L,i,d,e. i < d → subst L (#i) d e (#i)
| subst_lref_O : ∀L,V,e. 0 < e → subst (L. ♭Abbr V) #0 0 e V
| subst_lref_S : ∀L,I,V,i,T1,T2,d,e.
- d ≤ i → i < d + e → subst L #i d e T1 → [d,1]↑ T1 ≡ T2 →
+ d ≤ i → i < d + e → subst L #i d e T1 → ↑[d,1] T1 ≡ T2 →
subst (L. ♭I V) #(i + 1) (d + 1) e T2
| subst_lref_ge: ∀L,i,d,e. d + e ≤ i → subst L (#i) d e (#(i - e))
| subst_con2 : ∀L,I,V1,V2,T1,T2,d,e.
interpretation "telescopic substritution" 'RSubst L T1 d e T2 = (subst L T1 d e T2).
-lemma subst_lift_inv: ∀d,e,T1,T2. [d,e]↑ T1 ≡ T2 → ∀L. [d,e]← L / T2 ≡ T1.
+lemma subst_lift_inv: ∀d,e,T1,T2. ↑[d,e] T1 ≡ T2 → ∀L. L ⊢ ↓[d,e] T2 ≡ T1.
#d #e #T1 #T2 #H elim H -H d e T1 T2 /2/
#i #d #e #Hdi #L >(minus_plus_m_m i e) in ⊢ (? ? ? ? ? %) /3/ (**) (* use \ldots *)
qed.
| thin_thin: ∀L1,L2,I,V,e.
thin L1 0 e L2 → thin (L1. ♭I V) 0 (e + 1) L2
| thin_skip: ∀L1,L2,I,V1,V2,d,e.
- thin L1 d e L2 → [d,e]← L1 / V1 ≡ V2 →
+ thin L1 d e L2 → L1 ⊢ ↓[d,e] V1 ≡ V2 →
thin (L1. ♭I V1) (d + 1) e (L2. ♭I V2)
.
-interpretation "thinning" 'RThin L1 d e L2 = (thin L1 d e L2).
+interpretation "thinning" 'RSubst L1 d e L2 = (thin L1 d e L2).