(* This file was automatically generated: do not edit *********************)
-include "LambdaDelta-1/subst/defs.ma".
+include "Basic-1/subst/defs.ma".
theorem subst_sort:
\forall (v: T).(\forall (d: nat).(\forall (k: nat).(eq T (subst d v (TSort
\def
\lambda (_: T).(\lambda (_: nat).(\lambda (k: nat).(refl_equal T (TSort
k)))).
+(* COMMENTS
+Initial nodes: 13
+END *)
theorem subst_lref_lt:
\forall (v: T).(\forall (d: nat).(\forall (i: nat).((lt i d) \to (eq T
\Rightarrow (TLRef i) | false \Rightarrow (match (blt d i) with [true
\Rightarrow (TLRef (pred i)) | false \Rightarrow (lift d O v)])]) (TLRef i)))
(refl_equal T (TLRef i)) (blt i d) (lt_blt d i H))))).
+(* COMMENTS
+Initial nodes: 73
+END *)
theorem subst_lref_eq:
\forall (v: T).(\forall (i: nat).(eq T (subst i v (TLRef i)) (lift i O v)))
T (match b with [true \Rightarrow (TLRef i) | false \Rightarrow (match b with
[true \Rightarrow (TLRef (pred i)) | false \Rightarrow (lift i O v)])]) (lift
i O v))) (refl_equal T (lift i O v)) (blt i i) (le_bge i i (le_n i)))).
+(* COMMENTS
+Initial nodes: 71
+END *)
theorem subst_lref_gt:
\forall (v: T).(\forall (d: nat).(\forall (i: nat).((lt d i) \to (eq T
\Rightarrow (TLRef (pred i)) | false \Rightarrow (lift d O v)]) (TLRef (pred
i)))) (refl_equal T (TLRef (pred i))) (blt d i) (lt_blt i d H)) (blt i d)
(le_bge d i (lt_le_weak d i H)))))).
+(* COMMENTS
+Initial nodes: 130
+END *)
theorem subst_head:
\forall (k: K).(\forall (w: T).(\forall (u: T).(\forall (t: T).(\forall (d:
\def
\lambda (k: K).(\lambda (w: T).(\lambda (u: T).(\lambda (t: T).(\lambda (d:
nat).(refl_equal T (THead k (subst d w u) (subst (s k d) w t))))))).
+(* COMMENTS
+Initial nodes: 37
+END *)