(* Basic eliminators ********************************************************)
lemma csna_ind: ∀L. ∀R:predicate term.
- (â\88\80T1. L â\8a¢ â¬\87â¬\87* T1 →
- (∀T2. L ⊢ T1 ➡* T2 → (T1 = T2 → False) → R T2) → R T1
+ (â\88\80T1. L â\8a¢ â¬\8aâ¬\8a* T1 →
+ (∀T2. L ⊢ T1 ➡* T2 → (T1 = T2 → ⊥) → R T2) → R T1
) →
- â\88\80T. L â\8a¢ â¬\87â¬\87* T → R T.
+ â\88\80T. L â\8a¢ â¬\8aâ¬\8a* T → R T.
#L #R #H0 #T1 #H elim H -T1 #T1 #HT1 #IHT1
@H0 -H0 /3 width=1/ -IHT1 /4 width=1/
qed-.
(* Basic_1: was: sn3_intro *)
lemma csna_intro: ∀L,T1.
- (∀T2. L ⊢ T1 ➡* T2 → (T1 = T2 → False) → L ⊢ ⬇⬇* T2) → L ⊢ ⬇⬇* T1.
-#L #T1 #H
-@(SN_intro … H)
-qed.
+ (∀T2. L ⊢ T1 ➡* T2 → (T1 = T2 → ⊥) → L ⊢ ⬊⬊* T2) → L ⊢ ⬊⬊* T1.
+/4 width=1/ qed.
fact csna_intro_aux: ∀L,T1.
- (∀T,T2. L ⊢ T ➡* T2 → T1 = T → (T1 = T2 → False) → L ⊢ ⬇⬇* T2) → L ⊢ ⬇⬇* T1.
+ (∀T,T2. L ⊢ T ➡* T2 → T1 = T → (T1 = T2 → ⊥) → L ⊢ ⬊⬊* T2) → L ⊢ ⬊⬊* T1.
/4 width=3/ qed-.
(* Basic_1: was: sn3_pr3_trans (old version) *)
-lemma csna_cprs_trans: â\88\80L,T1. L â\8a¢ â¬\87â¬\87* T1 â\86\92 â\88\80T2. L â\8a¢ T1 â\9e¡* T2 â\86\92 L â\8a¢ â¬\87â¬\87* T2.
+lemma csna_cprs_trans: â\88\80L,T1. L â\8a¢ â¬\8aâ¬\8a* T1 â\86\92 â\88\80T2. L â\8a¢ T1 â\9e¡* T2 â\86\92 L â\8a¢ â¬\8aâ¬\8a* T2.
#L #T1 #H elim H -T1 #T1 #HT1 #IHT1 #T2 #HLT12
@csna_intro #T #HLT2 #HT2
elim (term_eq_dec T1 T2) #HT12
(* Basic_1: was: sn3_pr2_intro (old version) *)
lemma csna_intro_cpr: ∀L,T1.
- (∀T2. L ⊢ T1 ➡ T2 → (T1 = T2 → False) → L ⊢ ⬇⬇* T2) →
- L â\8a¢ â¬\87â¬\87* T1.
+ (∀T2. L ⊢ T1 ➡ T2 → (T1 = T2 → ⊥) → L ⊢ ⬊⬊* T2) →
+ L â\8a¢ â¬\8aâ¬\8a* T1.
#L #T1 #H
@csna_intro_aux #T #T2 #H @(cprs_ind_dx … H) -T
[ -H #H destruct #H
(* Main properties **********************************************************)
-theorem csn_csna: â\88\80L,T. L â\8a¢ â¬\87* T â\86\92 L â\8a¢ â¬\87â¬\87* T.
+theorem csn_csna: â\88\80L,T. L â\8a¢ â¬\8a* T â\86\92 L â\8a¢ â¬\8aâ¬\8a* T.
#L #T #H @(csn_ind … H) -T /4 width=1/
qed.
-theorem csna_csn: â\88\80L,T. L â\8a¢ â¬\87â¬\87* T â\86\92 L â\8a¢ â¬\87* T.
+theorem csna_csn: â\88\80L,T. L â\8a¢ â¬\8aâ¬\8a* T â\86\92 L â\8a¢ â¬\8a* T.
#L #T #H @(csna_ind … H) -T /4 width=1/
qed.
(* Basic_1: was: sn3_pr3_trans *)
-lemma csn_cprs_trans: â\88\80L,T1. L â\8a¢ â¬\87* T1 â\86\92 â\88\80T2. L â\8a¢ T1 â\9e¡* T2 â\86\92 L â\8a¢ â¬\87* T2.
+lemma csn_cprs_trans: â\88\80L,T1. L â\8a¢ â¬\8a* T1 â\86\92 â\88\80T2. L â\8a¢ T1 â\9e¡* T2 â\86\92 L â\8a¢ â¬\8a* T2.
/4 width=3/ qed.
(* Main eliminators *********************************************************)
lemma csn_ind_alt: ∀L. ∀R:predicate term.
- (â\88\80T1. L â\8a¢ â¬\87* T1 →
- (∀T2. L ⊢ T1 ➡* T2 → (T1 = T2 → False) → R T2) → R T1
+ (â\88\80T1. L â\8a¢ â¬\8a* T1 →
+ (∀T2. L ⊢ T1 ➡* T2 → (T1 = T2 → ⊥) → R T2) → R T1
) →
- â\88\80T. L â\8a¢ â¬\87* T → R T.
+ â\88\80T. L â\8a¢ â¬\8a* T → R T.
#L #R #H0 #T1 #H @(csna_ind … (csn_csna … H)) -T1 #T1 #HT1 #IHT1
@H0 -H0 /2 width=1/ -HT1 /3 width=1/
qed-.