lemma csn_ind: ∀L. ∀R:predicate term.
(∀T1. L ⊢ ⬇* T1 →
- (∀T2. L ⊢ T1 ➡ T2 → (T1 = T2 → False) → R T2) →
+ (∀T2. L ⊢ T1 ➡ T2 → (T1 = T2 → ⊥) → R T2) →
R T1
) →
∀T. L ⊢ ⬇* T → R T.
(* Basic_1: was: sn3_pr2_intro *)
lemma csn_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.
(* Basic_1: was: sn3_nf2 *)
-lemma csn_cnf: ∀L,T. L ⊢ 𝐍[T] → L ⊢ ⬇* T.
+lemma csn_cnf: ∀L,T. L ⊢ 𝐍⦃T⦄ → L ⊢ ⬇* T.
/2 width=1/ qed.
lemma csn_cpr_trans: ∀L,T1. L ⊢ ⬇* T1 → ∀T2. L ⊢ T1 ➡ T2 → L ⊢ ⬇* T2.
(* Basic_1: removed theorems 14:
sn3_cdelta
- sn3_gen_cflat sn3_cflat sn3_cpr3_trans sn3_shift sn3_change
- sn3_appl_cast sn3_appl_beta sn3_appl_lref sn3_appl_abbr
- sn3_appl_appls sn3_bind sn3_appl_bind sn3_appls_bind
+ sn3_gen_cflat sn3_cflat sn3_cpr3_trans sn3_shift sn3_change
+ sn3_appl_cast sn3_appl_beta sn3_appl_lref sn3_appl_abbr
+ sn3_appl_appls sn3_bind sn3_appl_bind sn3_appls_bind
*)