set "baseuri" "cic:/matita/tests/absurd/".
alias num (instance 0) = "natural number".
-alias symbol "eq" (instance 0) = "leibnitz's equality".
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
alias id "not" = "cic:/Coq/Init/Logic/not.con".
(* test _without_ the WHD on the apply argument *)
-alias symbol "eq" (instance 0) = "leibnitz's equality".
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
theorem a:
\forall A:Set.
alias id "nat" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)".
alias num (instance 0) = "natural number".
-alias symbol "and" (instance 0) = "logical and".
-alias symbol "eq" (instance 0) = "leibnitz's equality".
-alias symbol "plus" (instance 0) = "natural plus".
+alias symbol "and" (instance 0) = "Coq's logical and".
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
+alias symbol "plus" (instance 0) = "Coq's natural plus".
theorem stupid:
alias id "O" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/1)".
alias id "S" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/2)".
alias id "nat" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)".
-alias symbol "eq" (instance 0) = "leibnitz's equality".
-alias symbol "minus" (instance 0) = "natural minus".
-alias symbol "plus" (instance 0) = "natural plus".
-alias symbol "times" (instance 0) = "natural times".
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
+alias symbol "minus" (instance 0) = "Coq's natural minus".
+alias symbol "plus" (instance 0) = "Coq's natural plus".
+alias symbol "times" (instance 0) = "Coq's natural times".
theorem a : \forall x,y:nat. x*x+(S y) = O - x.
intros.
auto depth = 3.
set "baseuri" "cic:/matita/tests/change/".
alias num (instance 0) = "natural number".
-alias symbol "eq" (instance 0) = "leibnitz's equality".
-alias symbol "plus" (instance 0) = "natural plus".
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
+alias symbol "plus" (instance 0) = "Coq's natural plus".
alias id "nat" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)".
theorem stupid:
change in \vdash (? ? % ?) with 5.
rewrite < H in \vdash (? ? % ?).
reflexivity.
-qed.
\ No newline at end of file
+qed.
set "baseuri" "cic:/matita/tests/clear".
alias num (instance 0) = "natural number".
-alias symbol "eq" (instance 0) = "leibnitz's equality".
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
alias id "True" = "cic:/Coq/Init/Logic/True.ind#xpointer(1/1)".
set "baseuri" "cic:/matita/tests/clearbody".
alias num (instance 0) = "natural number".
-alias symbol "eq" (instance 0) = "leibnitz's equality".
-alias symbol "plus" (instance 0) = "natural plus".
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
+alias symbol "plus" (instance 0) = "Coq's natural plus".
theorem stupid :
coercion nat2int.
definition fst \def \lambda x,y:int.x.
-alias symbol "eq" (instance 0) = "leibnitz's equality".
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
theorem a: fst O one = fst (positive O) (next one).
reflexivity.
*)
alias num (instance 0) = "natural number".
-alias symbol "eq" (instance 0) = "leibnitz's equality".
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
theorem a:0=0.
(* nota *)
set "baseuri" "cic:/matita/tests/constructor".
alias num (instance 0) = "natural number".
-alias symbol "eq" (instance 0) = "leibnitz's equality".
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
theorem stupid: 1 = 1.
alias id "True" = "cic:/Coq/Init/Logic/True.ind#xpointer(1/1)".
alias id "not" = "cic:/Coq/Init/Logic/not.con".
alias num (instance 0) = "natural number".
-alias symbol "eq" (instance 0) = "leibnitz's equality".
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
set "baseuri" "cic:/matita/tests/cut".
alias num (instance 0) = "natural number".
-alias symbol "eq" (instance 0) = "leibnitz's equality".
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
theorem stupid: 3 = 3.
cut 3 = 3.
assumption.
reflexivity.
qed.
-
\ No newline at end of file
+
(**************************************************************************)
set "baseuri" "cic:/matita/tests/decompose".
-alias symbol "and" (instance 0) = "logical and".
-alias symbol "or" (instance 0) = "logical or".
+alias symbol "and" (instance 0) = "Coq's logical and".
+alias symbol "or" (instance 0) = "Coq's logical or".
set "baseuri" "cic:/matita/tests/discriminate".
alias id "not" = "cic:/Coq/Init/Logic/not.con".
alias num (instance 0) = "natural number".
-alias symbol "eq" (instance 0) = "leibnitz's equality".
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
theorem stupid:
| Next : stupidtype \to stupidtype
| Pair : stupidtype \to stupidtype \to stupidtype.
-alias symbol "eq" (instance 0) = "leibnitz's equality".
-alias symbol "exists" (instance 0) = "exists".
-alias symbol "or" (instance 0) = "logical or".
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
+alias symbol "exists" (instance 0) = "Coq's exists".
+alias symbol "or" (instance 0) = "Coq's logical or".
alias num (instance 0) = "natural number".
alias id "True" = "cic:/Coq/Init/Logic/True.ind#xpointer(1/1)".
alias id "refl_equal" = "cic:/Coq/Init/Logic/eq.ind#xpointer(1/1/1)".
alias id "False" = "cic:/Coq/Init/Logic/False.ind#xpointer(1/1)".
alias id "True" = "cic:/Coq/Init/Logic/True.ind#xpointer(1/1)".
-alias symbol "and" (instance 0) = "logical and".
-alias symbol "eq" (instance 0) = "leibnitz's equality".
-alias symbol "exists" (instance 0) = "exists".
+alias symbol "and" (instance 0) = "Coq's logical and".
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
+alias symbol "exists" (instance 0) = "Coq's exists".
definition is_S: nat \to Prop \def
\lambda n. match n with
set "baseuri" "cic:/matita/tests/fold".
alias id "nat" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)".
alias num (instance 0) = "natural number".
-alias symbol "eq" (instance 0) = "leibnitz's equality".
-alias symbol "plus" (instance 0) = "natural plus".
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
+alias symbol "plus" (instance 0) = "Coq's natural plus".
theorem t: \forall x:nat. 0+x=x.
intro.
simplify in match (0+x) in \vdash (? ? % ?).
set "baseuri" "cic:/matita/generalize".
alias num (instance 0) = "natural number".
-alias symbol "eq" (instance 0) = "leibnitz's equality".
-alias symbol "plus" (instance 0) = "natural plus".
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
+alias symbol "plus" (instance 0) = "Coq's natural plus".
alias id "plus_comm" = "cic:/Coq/Arith/Plus/plus_comm.con".
alias id "S" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/2)".
theorem test2: \forall x. x + 4 = 4 + x.
generalize in match 4.
exact plus_comm.
-qed.
\ No newline at end of file
+qed.
leO : le n n
| leS : \forall m. le n m \to le n (S m).
-alias symbol "eq" (instance 0) = "leibnitz's equality".
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
theorem test_inversion: \forall n. le n O \to n=O.
intros.
set "baseuri" "cic:/matita/tests/paramodulation".
alias id "nat" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)".
-alias symbol "eq" (instance 0) = "leibnitz's equality".
-alias symbol "plus" (instance 0) = "natural plus".
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
+alias symbol "plus" (instance 0) = "Coq's natural plus".
alias num (instance 0) = "natural number".
-alias symbol "times" (instance 0) = "natural times".
+alias symbol "times" (instance 0) = "Coq's natural times".
theorem para1:
\forall n,m,n1,m1:nat.
set "baseuri" "cic:/matita/tests/replace/".
alias id "nat" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)".
alias num (instance 0) = "natural number".
-alias symbol "eq" (instance 0) = "leibnitz's equality".
-alias symbol "plus" (instance 0) = "natural plus".
-alias symbol "times" (instance 0) = "natural times".
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
+alias symbol "plus" (instance 0) = "Coq's natural plus".
+alias symbol "times" (instance 0) = "Coq's natural times".
alias id "mult_n_O" = "cic:/Coq/Init/Peano/mult_n_O.con".
alias id "plus_n_O" = "cic:/Coq/Init/Peano/plus_n_O.con".
alias id "nat" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)".
alias num (instance 0) = "natural number".
-alias symbol "eq" (instance 0) = "leibnitz's equality".
-alias symbol "plus" (instance 0) = "natural plus".
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
+alias symbol "plus" (instance 0) = "Coq's natural plus".
alias id "plus_n_O" = "cic:/Coq/Init/Peano/plus_n_O.con".
theorem a:
theorem foo: \forall n. n = n + 0.
intros.
rewrite < t; reflexivity.
-qed.
\ No newline at end of file
+qed.
set "baseuri" "cic:/matita/tests/simpl/".
alias id "not" = "cic:/Coq/Init/Logic/not.con".
-alias symbol "eq" (instance 0) = "leibnitz's equality".
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
theorem a :
\forall A:Set.
\forall x,y : A.
set "baseuri" "cic:/matita/tests/test2/".
alias id "nat" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)".
-alias symbol "and" (instance 0) = "logical and".
-alias symbol "eq" (instance 0) = "leibnitz's equality".
+alias symbol "and" (instance 0) = "Coq's logical and".
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
theorem a:\forall x:nat.x=x\land x=x.
intro.
split.
set "baseuri" "cic:/matita/tests/test3/".
-alias symbol "eq" (instance 0) = "leibnitz's equality".
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
theorem a:\forall x.x=x.
alias id "nat" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)".
exact nat.
reflexivity.
qed.
alias num (instance 0) = "natural number".
-alias symbol "times" (instance 0) = "natural times".
+alias symbol "times" (instance 0) = "Coq's natural times".
theorem b:\forall p:nat. p * 0=0.
intro.
*)
alias num (instance 0) = "natural number".
-alias symbol "eq" (instance 0) = "leibnitz's equality".
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
theorem a:0=0.
(* nota *)