(* Basic_inversion lemmas **************************************************)
-lemma liftsb_inv_unit_sn: â\88\80f,I,Z2. â¬\86*[f] BUnit I ≘ Z2 → Z2 = BUnit I.
+lemma liftsb_inv_unit_sn: â\88\80f,I,Z2. â\87§*[f] BUnit I ≘ Z2 → Z2 = BUnit I.
/2 width=2 by ext2_inv_unit_sn/ qed-.
-lemma liftsb_inv_pair_sn: â\88\80f:rtmap. â\88\80Z2,I,V1. â¬\86*[f] BPair I V1 ≘ Z2 →
- â\88\83â\88\83V2. â¬\86*[f] V1 ≘ V2 & Z2 = BPair I V2.
+lemma liftsb_inv_pair_sn: â\88\80f:rtmap. â\88\80Z2,I,V1. â\87§*[f] BPair I V1 ≘ Z2 →
+ â\88\83â\88\83V2. â\87§*[f] V1 ≘ V2 & Z2 = BPair I V2.
/2 width=1 by ext2_inv_pair_sn/ qed-.
-lemma liftsb_inv_unit_dx: â\88\80f,I,Z1. â¬\86*[f] Z1 ≘ BUnit I → Z1 = BUnit I.
+lemma liftsb_inv_unit_dx: â\88\80f,I,Z1. â\87§*[f] Z1 ≘ BUnit I → Z1 = BUnit I.
/2 width=2 by ext2_inv_unit_dx/ qed-.
-lemma liftsb_inv_pair_dx: â\88\80f:rtmap. â\88\80Z1,I,V2. â¬\86*[f] Z1 ≘ BPair I V2 →
- â\88\83â\88\83V1. â¬\86*[f] V1 ≘ V2 & Z1 = BPair I V1.
+lemma liftsb_inv_pair_dx: â\88\80f:rtmap. â\88\80Z1,I,V2. â\87§*[f] Z1 ≘ BPair I V2 →
+ â\88\83â\88\83V1. â\87§*[f] V1 ≘ V2 & Z1 = BPair I V1.
/2 width=1 by ext2_inv_pair_dx/ qed-.
(* Basic properties *********************************************************)
-lemma liftsb_eq_repl_back: â\88\80I1,I2. eq_repl_back â\80¦ (λf. â¬\86*[f] I1 ≘ I2).
+lemma liftsb_eq_repl_back: â\88\80I1,I2. eq_repl_back â\80¦ (λf. â\87§*[f] I1 ≘ I2).
#I1 #I2 #f1 * -I1 -I2 /3 width=3 by lifts_eq_repl_back, ext2_pair/
qed-.
lemma liftsb_refl: ∀f. 𝐈⦃f⦄ → reflexive … (liftsb f).
/3 width=1 by lifts_refl, ext2_refl/ qed.
-lemma liftsb_total: â\88\80I1,f. â\88\83I2. â¬\86*[f] I1 ≘ I2.
+lemma liftsb_total: â\88\80I1,f. â\88\83I2. â\87§*[f] I1 ≘ I2.
* [2: #I #T1 #f elim (lifts_total T1 f) ]
/3 width=2 by ext2_unit, ext2_pair, ex_intro/
qed-.
-lemma liftsb_split_trans: â\88\80f,I1,I2. â¬\86*[f] I1 ≘ I2 →
+lemma liftsb_split_trans: â\88\80f,I1,I2. â\87§*[f] I1 ≘ I2 →
∀f1,f2. f2 ⊚ f1 ≘ f →
- â\88\83â\88\83I. â¬\86*[f1] I1 â\89\98 I & â¬\86*[f2] I ≘ I2.
+ â\88\83â\88\83I. â\87§*[f1] I1 â\89\98 I & â\87§*[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/
(* Basic forward lemmas *****************************************************)
-lemma liftsb_fwd_isid: â\88\80f,I1,I2. â¬\86*[f] I1 ≘ I2 → 𝐈⦃f⦄ → I1 = I2.
+lemma liftsb_fwd_isid: â\88\80f,I1,I2. â\87§*[f] I1 ≘ I2 → 𝐈⦃f⦄ → I1 = I2.
#f #I1 #I2 * -I1 -I2 /3 width=3 by lifts_fwd_isid, eq_f2/
qed-.