partial commit in static_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / syntax / cl_restricted_weight.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/cl_restricted_weight.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/cl_restricted_weight.ma
index 31c3f7adc28ee03ce44cae6fbab1da9c5f05e2a7..62ce9d6fca80fa26e839b01a0fb9b16dc3bba84c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/syntax/cl_restricted_weight.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/cl_restricted_weight.ma
@@ -17,35 +17,35 @@ include "static_2/syntax/lenv_weight.ma".
 
 (* WEIGHT OF A RESTRICTED CLOSURE *******************************************)
 
-definition rfw: lenv → term → ? ≝ λL,T. ♯{L} + ♯{T}.
+definition rfw: lenv → term → ? ≝ λL,T. ♯❨L❩ + ♯❨T❩.
 
 interpretation "weight (restricted closure)" 'Weight L T = (rfw L T).
 
 (* Basic properties *********************************************************)
 
 (* Basic_1: was: flt_shift *)
-lemma rfw_shift: ∀p,I,K,V,T. ♯{K.ⓑ{I}V, T} < ♯{K, ⓑ{p,I}V.T}.
-normalize /2 width=1 by monotonic_le_plus_r/
+lemma rfw_shift: ∀p,I,K,V,T. ♯❨K.ⓑ[I]V,T❩ < ♯❨K,ⓑ[p,I]V.T❩.
+normalize /2 width=1 by nle_plus_bi_sn/
 qed.
 
-lemma rfw_clear: ∀p,I1,I2,K,V,T. ♯{K.ⓤ{I1}, T} < ♯{K, ⓑ{p,I2}V.T}.
-normalize /4 width=1 by monotonic_le_plus_r, le_S_S/
+lemma rfw_clear: ∀p,I1,I2,K,V,T. ♯❨K.ⓤ[I1],T❩ < ♯❨K,ⓑ[p,I2]V.T❩.
+normalize /4 width=1 by nle_plus_bi_sn, nle_succ_bi/
 qed.
 
-lemma rfw_tpair_sn: ∀I,L,V,T. ♯{L, V} < ♯{L, ②{I}V.T}.
+lemma rfw_tpair_sn: ∀I,L,V,T. ♯❨L,V❩ < ♯❨L,②[I]V.T❩.
 normalize in ⊢ (?→?→?→?→?%%); //
 qed.
 
-lemma rfw_tpair_dx: ∀I,L,V,T. ♯{L, T} < ♯{L, ②{I}V.T}.
+lemma rfw_tpair_dx: ∀I,L,V,T. ♯❨L,T❩ < ♯❨L,②[I]V.T❩.
 normalize in ⊢ (?→?→?→?→?%%); //
 qed.
 
-lemma rfw_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/
+lemma rfw_lpair_sn: ∀I,L,V,T. ♯❨L,V❩ < ♯❨L.ⓑ[I]V,T❩.
+normalize /3 width=1 by nlt_plus_bi_dx, nle_plus_bi_sn/
 qed.
 
-lemma rfw_lpair_dx: ∀I,L,V,T. ♯{L, T} < ♯{L.ⓑ{I}V, T}.
-normalize /3 width=1 by monotonic_lt_plus_l, monotonic_le_plus_r/
+lemma rfw_lpair_dx: ∀I,L,V,T. ♯❨L,T❩ < ♯❨L.ⓑ[I]V,T❩.
+normalize /3 width=1 by nlt_plus_bi_dx, nle_plus_bi_sn/
 qed.
 
 (* Basic_1: removed theorems 7: