lemma csna_ind: ∀L. ∀R:predicate term.
(∀T1. L ⊢ ⬇⬇* T1 →
- (∀T2. L ⊢ T1 ➡* T2 → (T1 = T2 → False) → R T2) → R T1
+ (∀T2. L ⊢ T1 ➡* T2 → (T1 = T2 → ⊥) → R T2) → R T1
) →
∀T. L ⊢ ⬇⬇* T → R T.
#L #R #H0 #T1 #H elim H -T1 #T1 #HT1 #IHT1
(* 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) *)
(* Basic_1: was: sn3_pr2_intro (old version) *)
lemma csna_intro_cpr: ∀L,T1.
- (∀T2. L ⊢ T1 ➡ T2 → (T1 = T2 → False) → L ⊢ ⬇⬇* T2) →
+ (∀T2. L ⊢ T1 ➡ T2 → (T1 = T2 → ⊥) → L ⊢ ⬇⬇* T2) →
L ⊢ ⬇⬇* T1.
#L #T1 #H
@csna_intro_aux #T #T2 #H @(cprs_ind_dx … H) -T
lemma csn_ind_alt: ∀L. ∀R:predicate term.
(∀T1. L ⊢ ⬇* T1 →
- (∀T2. L ⊢ T1 ➡* T2 → (T1 = T2 → False) → R T2) → R T1
+ (∀T2. L ⊢ T1 ➡* T2 → (T1 = T2 → ⊥) → R T2) → R T1
) →
∀T. L ⊢ ⬇* T → R T.
#L #R #H0 #T1 #H @(csna_ind … (csn_csna … H)) -T1 #T1 #HT1 #IHT1