interpretation "generic relocation (binder for local environments)"
'RLiftStar f I1 I2 = (liftsb f I1 I2).
interpretation "generic relocation (binder for local environments)"
'RLiftStar f I1 I2 = (liftsb f I1 I2).
-lemma liftsb_inv_unit_sn: ∀f,I,Z2. ⬆*[f] BUnit I ≘ Z2 → Z2 = BUnit I.
+lemma liftsb_inv_unit_sn (f):
+ ∀I,Z2. ⇧*[f] BUnit I ≘ Z2 → Z2 = BUnit I.
-lemma liftsb_inv_pair_sn: ∀f:rtmap. ∀Z2,I,V1. ⬆*[f] BPair I V1 ≘ Z2 →
- ∃∃V2. ⬆*[f] V1 ≘ V2 & Z2 = BPair I V2.
+lemma liftsb_inv_pair_sn (f):
+ ∀Z2,I,V1. ⇧*[f] BPair I V1 ≘ Z2 →
+ ∃∃V2. ⇧*[f] V1 ≘ V2 & Z2 = BPair I V2.
-lemma liftsb_inv_unit_dx: ∀f,I,Z1. ⬆*[f] Z1 ≘ BUnit I → Z1 = BUnit I.
+lemma liftsb_inv_unit_dx (f):
+ ∀I,Z1. ⇧*[f] Z1 ≘ BUnit I → Z1 = BUnit I.
-lemma liftsb_inv_pair_dx: ∀f:rtmap. ∀Z1,I,V2. ⬆*[f] Z1 ≘ BPair I V2 →
- ∃∃V1. ⬆*[f] V1 ≘ V2 & Z1 = BPair I V1.
+lemma liftsb_inv_pair_dx (f):
+ ∀Z1,I,V2. ⇧*[f] Z1 ≘ BPair I V2 →
+ ∃∃V1. ⇧*[f] V1 ≘ V2 & Z1 = BPair I V1.
/2 width=1 by ext2_inv_pair_dx/ qed-.
(* Basic properties *********************************************************)
/2 width=1 by ext2_inv_pair_dx/ qed-.
(* Basic properties *********************************************************)
* [2: #I #T1 #f elim (lifts_total T1 f) ]
/3 width=2 by ext2_unit, ext2_pair, ex_intro/
qed-.
* [2: #I #T1 #f elim (lifts_total T1 f) ]
/3 width=2 by ext2_unit, ext2_pair, ex_intro/
qed-.
-lemma liftsb_split_trans: ∀f,I1,I2. ⬆*[f] I1 ≘ I2 →
- ∀f1,f2. f2 ⊚ f1 ≘ f →
- ∃∃I. ⬆*[f1] I1 ≘ I & ⬆*[f2] I ≘ I2.
+lemma liftsb_split_trans (f):
+ ∀I1,I2. ⇧*[f] I1 ≘ I2 → ∀f1,f2. f2 ⊚ f1 ≘ f →
+ ∃∃I. ⇧*[f1] I1 ≘ I & ⇧*[f2] I ≘ I2.
#f #I1 #I2 * -I1 -I2 /2 width=3 by ext2_unit, ex2_intro/
#I #V1 #V2 #HV12 #f1 #f2 #Hf elim (lifts_split_trans … HV12 … Hf) -f
/3 width=3 by ext2_pair, ex2_intro/
#f #I1 #I2 * -I1 -I2 /2 width=3 by ext2_unit, ex2_intro/
#I #V1 #V2 #HV12 #f1 #f2 #Hf elim (lifts_split_trans … HV12 … Hf) -f
/3 width=3 by ext2_pair, ex2_intro/
-lemma liftsb_fwd_isid: ∀f,I1,I2. ⬆*[f] I1 ≘ I2 → 𝐈⦃f⦄ → I1 = I2.
+lemma liftsb_fwd_isid (f):
+ ∀I1,I2. ⇧*[f] I1 ≘ I2 → 𝐈❨f❩ → I1 = I2.