lambdadelta

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / grammar / cl_weight.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/grammar/cl_weight.ma b/matita/matita/contribs/lambdadelta/basic_2/grammar/cl_weight.ma
index d9569d4d57ffd3a236d7d591c72688a435b6160b..66c8d0fb7c45d319b82f75be2e47e09e0816b0d7 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/grammar/cl_weight.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/grammar/cl_weight.ma
@@ -12,57 +12,37 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "basic_2/notation/functions/weight_2.ma".
 include "basic_2/grammar/lenv_weight.ma".
 include "basic_2/grammar/cl_shift.ma".
 
 (* WEIGHT OF A CLOSURE ******************************************************)
 
-definition fw: lenv → term → ? ≝ λL,T. #{L} + #{T}.
+definition fw: lenv → term → ? ≝ λL,T. ♯{L} + ♯{T}.
 
 interpretation "weight (closure)" 'Weight L T = (fw L T).
 
 (* Basic properties *********************************************************)
 
-(* Basic_1: was: flt_wf__q_ind *)
-
-(* Basic_1: was: flt_wf_ind *)
-axiom fw_ind: ∀R:relation2 lenv term.
-              (∀L2,T2. (∀L1,T1. #{L1,T1} < #{L2,T2} → R L1 T1) → R L2 T2) →
-              ∀L,T. R L T.
-
 (* Basic_1: was: flt_shift *)
-lemma fw_shift: ∀a,K,I,V,T. #{K. ⓑ{I} V, T} < #{K, ⓑ{a,I} V. T}.
+lemma fw_shift: ∀a,K,I,V,T. ♯{K. ⓑ{I} V, T} < ♯{K, ⓑ{a,I} V. T}.
 normalize //
 qed.
 
-lemma tw_shift: ∀L,T. #{L, T} ≤ #{L @@ T}.
-#L elim L //
-#K #I #V #IHL #T
-@transitive_le [3: @IHL |2: /2 width=2/ | skip ]
-qed.
-
-lemma fw_tpair_sn: ∀I,L,V,T. #{L, V} < #{L, ②{I}V.T}.
+lemma fw_tpair_sn: ∀I,L,V,T. ♯{L, V} < ♯{L, ②{I}V.T}.
 normalize in ⊢ (?→?→?→?→?%%); //
 qed.
 
-lemma fw_tpair_dx: ∀I,L,V,T. #{L, T} < #{L, ②{I}V.T}.
+lemma fw_tpair_dx: ∀I,L,V,T. ♯{L, T} < ♯{L, ②{I}V.T}.
 normalize in ⊢ (?→?→?→?→?%%); //
 qed.
 
-lemma fw_tpair_dx_sn: ∀I1,I2,L,V1,V2,T. #{L, V2} < #{L, ②{I1}V1.②{I2}V2.T}.
-normalize in ⊢ (?→?→?→?→?→?→?%%); /2 width=1/
-qed.
-
-lemma fw_tpair_sn_sn_shift: ∀I,I1,I2,L,V1,V2,T.
-                            #{L.ⓑ{I}V1, T} < #{L, ②{I1}V1.②{I2}V2.T}.
-normalize in ⊢ (?→?→?→?→?→?→?→?%%); /3 width=1/ 
-qed.
-
-lemma fw_tpair_sn_dx_shift: ∀I,I1,I2,L,V1,V2,T.
-                            #{L.ⓑ{I}V2, T} < #{L, ②{I1}V1.②{I2}V2.T}.
-normalize in ⊢ (?→?→?→?→?→?→?→?%%); /2 width=1/
+lemma fw_lpair_sn: ∀I,L,V,T. ♯{L, V} < ♯{L.ⓑ{I}V, T}.
+normalize /3 width=1 by monotonic_lt_plus_l, monotonic_le_plus_r/ (**) (* auto too slow without trace *)
 qed.
 
-(* Basic_1: removed theorems 6:
-            flt_thead_sx flt_thead_dx flt_arith0 flt_arith1 flt_arith2 flt_trans
+(* Basic_1: removed theorems 7:
+            flt_thead_sx flt_thead_dx flt_trans
+            flt_arith0 flt_arith1 flt_arith2 flt_wf_ind
 *)
+(* Basic_1: removed local theorems 1: q_ind *)