(* *)
(**************************************************************************)
-set "baseuri" "cic:/matita/test/injection/".
-include "legacy/coq.ma".
+
+include "coq.ma".
alias id "nat" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)".
alias id "bool" = "cic:/Coq/Init/Datatypes/bool.ind#xpointer(1/1)".
theorem injection_test0: ∀n,n',m,m'. k0 n m = k0 n' m' → m = m'.
intros;
- injection H;
- assumption.
+ destruct H;
+ reflexivity.
qed.
inductive t : Type → Type :=
theorem injection_test1: ∀n,n'. k n = k n' → n = n'.
intros;
- injection H;
- assumption.
+ destruct H;
+ reflexivity.
qed.
inductive tt (A:Type) : Type -> Type :=
theorem injection_test2: ∀n,n',m,m'. k1 bool n n' = k1 bool m m' → n' = m'.
intros;
- injection H;
- assumption.
+ destruct H;
+ reflexivity.
qed.
inductive ttree : Type → Type :=
tempty: ttree nat
| tnode : ∀A. ttree A → ttree A → ttree A.
-(* CSC: there is an undecidable unification problem here:
- consider a constructor k : \forall x. f x -> i (g x)
- The head of the outtype of the injection MutCase should be (f ?1)
- such that (f ?1) unifies with (g d) [ where d is the Rel that binds
- the corresponding right parameter in the outtype ]
- Coq dodges the problem by generating an equality between sigma-types
- (that state the existence of a ?1 such that ...)
-theorem injection_test3:
- ∀t,t'. tnode nat t tempty = tnode nat t' tempty → t = t'.
- intros;
- injection H;
- assumption.
-qed.
-
-theorem injection_test3:
- ∀t,t'.
- tnode nat (tnode nat t t') tempty = tnode nat (tnode nat t' tempty) tempty →
- t = t'.
- intros;
- injection H;
-*)
-
theorem injection_test4:
∀n,n',m,m'. k1 bool (S n) (S (S m)) = k1 bool (S n') (S (S (S m'))) → m = S m'.
intros;
- injection H;
- assumption.
-qed.
\ No newline at end of file
+ destruct H;
+ reflexivity.
+qed.