alias id "plus_lt_le_compat" = "cic:/Coq/Arith/Plus/plus_lt_le_compat.con".
alias id "plus_lt_compat" = "cic:/Coq/Arith/Plus/plus_lt_compat.con".
alias id "lt_S_n" = "cic:/Coq/Arith/Lt/lt_S_n.con".
+alias id "minus_n_n" = "cic:/Coq/Arith/Minus/minus_n_n.con".
theorem f_equal: \forall A,B:Type. \forall f:A \to B.
\forall x,y:A. x = y \to f x = f y.
unfold not. intros. apply H. symmetry. assumption.
qed.
+theorem trans_eq : ∀A:Type.∀x,y,z:A.x=y→y=z→x=z.
+ intros;
+ transitivity y;
+ assumption.
+qed.
+
theorem plus_reg_l: \forall (n,m,p:nat). n + m = n + p \to m = p.
intros. apply plus_reg_l; auto.
qed.
intros. apply plus_le_reg_l; auto.
qed.
-definition sym_equal \def sym_eq.
-
default "equality"
cic:/Coq/Init/Logic/eq.ind
cic:/matita/LAMBDA-TYPES/Level-1/Base/ext/preamble/sym_eq.con
- cic:/Coq/Init/Logic/trans_eq.con
+ cic:/matita/LAMBDA-TYPES/Level-1/Base/ext/preamble/trans_eq.con
cic:/Coq/Init/Logic/eq_ind.con
cic:/Coq/Init/Logic/eq_ind_r.con
cic:/matita/LAMBDA-TYPES/Level-1/Base/ext/preamble/f_equal.con