more chosmetic

diff --git a/helm/software/matita/dama/sandwich.ma b/helm/software/matita/dama/sandwich.ma
index 95dd0d3cbc0c5add6a783457b962f96e791509ce..21499ee7230304e0f1188d36dace724e839fb6df 100644 (file)
--- a/helm/software/matita/dama/sandwich.ma
+++ b/helm/software/matita/dama/sandwich.ma
@@ -54,16 +54,16 @@ cases (H n3) (H7 H8); clear Lt_n1n3 Lt_n2n3 Lt_n1n2_n3 c H1 H2 H n1 n2;
 (* the main inequality *)
 cut (δ (xn n3) x ≤ δ (bn n3) x + δ (an n3) x + δ (an n3) x) as main_ineq; [2:
   apply (le_transitive ???? (mtineq ???? (an n3)));
-  lapply (le_mtri ????? H7 H8) as H9; clear H7 H8;
-  lapply (feq_plusr ? (- δ(xn n3) (bn n3)) ?? H9) as H10; clear H9;
   cut ( δ(an n3) (bn n3)+- δ(xn n3) (bn n3)≈( δ(an n3) (xn n3))) as H11; [2:
-    apply (Eq≈  (0 + δ(an n3) (xn n3)) ? (zero_neutral ??));
-    apply (Eq≈  (δ(an n3) (xn n3) + 0) ? (plus_comm ???));
-    apply (Eq≈  (δ(an n3) (xn n3) +  (-δ(xn n3) (bn n3) +  δ(xn n3) (bn n3))) ? (opp_inverse ??));
-    apply (Eq≈  (δ(an n3) (xn n3) +  (δ(xn n3) (bn n3) + -δ(xn n3) (bn n3))) ? (plus_comm ?? (δ(xn n3) (bn n3))));
-    apply (Eq≈  ? ? (eq_sym ??? (plus_assoc ????))); assumption;] clear H10;
-  apply (le_rewl ???  ( δ(an n3) (xn n3)+ δ(an n3) x) (msymmetric ??(an n3)(xn n3)));    
-  apply (le_rewl ???  (δ(an n3) (bn n3)+- δ(xn n3) (bn n3)+ δ(an n3) x) H11);
+    lapply (le_mtri ????? H7 H8) as H9; clear H7 H8;
+    lapply (feq_plusr ? (- δ(xn n3) (bn n3)) ?? H9) as H10; clear H9;
+    apply (Eq≈ (0 + δ(an n3) (xn n3)) ? (zero_neutral ??));
+    apply (Eq≈ (δ(an n3) (xn n3) + 0) ? (plus_comm ???));
+    apply (Eq≈ (δ(an n3) (xn n3) + (-δ(xn n3) (bn n3) +  δ(xn n3) (bn n3))) ? (opp_inverse ??));
+    apply (Eq≈ (δ(an n3) (xn n3) + (δ(xn n3) (bn n3) + -δ(xn n3) (bn n3))) ? (plus_comm ?? (δ(xn n3) (bn n3))));
+    apply (Eq≈ ?? (eq_sym ??? (plus_assoc ????))); assumption;]
+  apply (Le≪ (δ(an n3) (xn n3)+ δ(an n3) x) (msymmetric ??(an n3)(xn n3)));    
+  apply (Le≪ (δ(an n3) (bn n3)+- δ(xn n3) (bn n3)+ δ(an n3) x) H11);
   apply (Le≪ (- δ(xn n3) (bn n3)+ δ(an n3) (bn n3)+δ(an n3) x) (plus_comm ??(δ(an n3) (bn n3))));
   apply (Le≪ (- δ(xn n3) (bn n3)+ (δ(an n3) (bn n3)+δ(an n3) x)) (plus_assoc ????));
   apply (Le≪ ((δ(an n3) (bn n3)+δ(an n3) x)+- δ(xn n3) (bn n3)) (plus_comm ???));