Added examples.

[helm.git] / helm / gTopLevel / esempi / evars.cic

diff --git a/helm/gTopLevel/esempi/evars.cic b/helm/gTopLevel/esempi/evars.cic
new file mode 100644 (file)
index 0000000..9183cb1
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+++ b/helm/gTopLevel/esempi/evars.cic
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+alias nat          /Coq/Init/Datatypes/nat.ind#1/1
+alias eqT          /Coq/Init/Logic_Type/eqT.ind#1/1
+alias eq           /Coq/Init/Logic/Equality/eq.ind#1/1
+alias refl_equal   /Coq/Init/Logic/Equality/eq.ind#1/1/1
+alias eq_ind       /Coq/Init/Logic/Equality/eq_ind.con
+alias eq_ind_r     /Coq/Init/Logic/Logic_lemmas/eq_ind_r.con
+alias O            /Coq/Init/Datatypes/nat.ind#1/1/1
+alias S            /Coq/Init/Datatypes/nat.ind#1/1/2
+alias plus         /Coq/Init/Peano/plus.con
+alias mult         /Coq/Init/Peano/mult.con
+alias le           /Coq/Init/Peano/le.ind#1/1
+alias lt           /Coq/Init/Peano/lt.con
+alias not          /Coq/Init/Logic/not.con
+alias f_equal      /Coq/Init/Logic/Logic_lemmas/equality/f_equal.con
+alias le_trans     /Coq/Arith/Le/le_trans.con
+
+alias le_plus_plus /Coq/Arith/Plus/le_plus_plus.con
+alias le_reg_r     /Coq/Arith/Plus/le_reg_r.con
+alias le_reg_l     /Coq/Arith/Plus/le_reg_l.con
+
+alias plus_n_O     /Coq/Init/Peano/plus_n_O.con 
+
+!n:nat.!m:nat.(le n m)->(le (mult (S (S O)) n) (mult (S (S O)) m))
+
+(* Lo scopo dell'esercizio e' riuscire a effettuare la dimostrazione che *)
+(* (n <= m) -> (2*n <= 2*m) come la si farebbe su carta, ovvero:         *)
+(*                                                                       *)
+(*     2 * n                                                             *)
+(*  == n + n + 0     Simpl                                               *)
+(*  <= m + n + 0     le_reg_r because n <= m because hypothesis          *)
+(*  <= m + m + 0     le_reg_l because n + 0 <= m + 0 because le_reg_r    *)
+(*                    because hypothesis                                 *)
+(*  == 2 * m         Change                                              *)