- we weakened SAT3

[helm.git] / matita / matita / lib / lambda / sn.ma

diff --git a/matita/matita/lib/lambda/sn.ma b/matita/matita/lib/lambda/sn.ma
index 26b1f9e77690aafaafed20ad6121de8bb3a7943d..a9fbff3700afc50ae67e78db40b3e966bf60ebfd 100644 (file)
--- a/matita/matita/lib/lambda/sn.ma
+++ b/matita/matita/lib/lambda/sn.ma
@@ -12,41 +12,59 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "lambda/ext.ma".
+include "lambda/ext_lambda.ma".
 
-(* saturation conditions on an explicit subset ********************************)
+(* STRONGLY NORMALIZING TERMS *************************************************)
 
-definition SAT0 ≝ λP. ∀l,n. all P l → P (Appl (Sort n) l).
+(* SN(t) holds when t is strongly normalizing *)
+(* FG: we axiomatize it for now because we dont have reduction yet *)
+axiom SN: T → Prop.
 
-definition SAT1 ≝ λP. ∀l,i. all P l → P (Appl (Rel i) l).
+(* lists of strongly normalizing terms *)
+definition SNl ≝ all ? SN.
 
-definition SAT2 ≝ λ(P:?→Prop). ∀F,A,B,l. P B → P A → 
-                  P (Appl F[0:=A] l) → P (Appl (Lambda B F) (A::l)).
+(* saturation conditions ******************************************************)
 
-theorem SAT0_sort: ∀P,n. SAT0 P → P (Sort n).
-#P #n #H @(H (nil ?) …) //
-qed.
+definition CR1 ≝ λ(P:?→Prop). ∀M. P M → SN M.
 
-theorem SAT1_rel: ∀P,i. SAT1 P → P (Rel i).
-#P #i #H @(H (nil ?) …) //
+definition SAT0 ≝ λ(P:?→Prop). ∀n,l. SNl l → P (Appl (Sort n) l).
+
+definition SAT1 ≝ λ(P:?->Prop). ∀i,l. SNl l → P (Appl (Rel i) l).
+
+definition SAT2 ≝ λ(P:?→Prop). ∀N,L,M,l. SN N → SN L → 
+                  P (Appl M[0:=L] l) → P (Appl (Lambda N M) (L::l)).
+
+definition SAT3 ≝ λ(P:?→Prop). ∀M,N,l. P (Appl (D (App M N)) l) → 
+                               P (Appl (D M) (N::l)).
+
+definition SAT4 ≝ λ(P:?→Prop). ∀M. P M → P (D M).
+
+lemma SAT0_sort: ∀P,n. SAT0 P → P (Sort n).
+#P #n #HP @(HP n (nil ?) …) //
 qed.
 
-(* STRONGLY NORMALIZING TERMS *************************************************)
+lemma SAT1_rel: ∀P,i. SAT1 P → P (Rel i).
+#P #i #HP @(HP i (nil ?) …) //
+qed.
 
-(* SN(t) holds when t is strongly normalizing *)
-(* FG: we axiomatize it for now because we dont have reduction yet *)
-axiom SN: T → Prop.
+lemma SAT3_1: ∀P,M,N. SAT3 P → P (D (App M N)) → P (App (D M) N).
+#P #M #N #HP #H @(HP … ([])) @H
+qed.
 
-definition CR1 ≝ λ(P:?→Prop). ∀M. P M → SN M.
+(* axiomatization *************************************************************)
 
 axiom sn_sort: SAT0 SN.
 
 axiom sn_rel: SAT1 SN.
 
-axiom sn_lambda: ∀B,F. SN B → SN F → SN (Lambda B F).
-
 axiom sn_beta: SAT2 SN.
 
-(* FG: do we need this?
-axiom sn_lift: ∀t,k,p. SN t → SN (lift t p k).
-*)
+axiom sn_dapp: SAT3 SN.
+
+axiom sn_dummy: SAT4 SN.
+
+axiom sn_lambda: ∀N,M. SN N → SN M → SN (Lambda N M).
+
+axiom sn_prod: ∀N,M. SN N → SN M → SN (Prod N M).
+
+axiom sn_inv_app_1: ∀M,N. SN (App M N) → SN M.