CoqAt this moment I am just trying to run the code in the Coq Tutorial... The following e-script, corresponding to the section "Existential Quantification" of the tutorial, is not working as it should:
Here is its log: Welcome to Coq 8.1pl3 (Dec. 2007)
Coq < Reset Initial.
Coq < Section Predicate_calculus.
Coq < Variable D : Set.
D is assumed
Coq < Variable R : D -> D -> Prop.
R is assumed
Coq < Section R_sym_trans.
Coq < Hypothesis R_symmetric : forall x y:D, R x y -> R y x.
R_symmetric is assumed
Coq < Hypothesis R_transitive : forall x y z:D, R x y -> R y z -> R x z.
R_transitive is assumed
Coq < Lemma refl_if : forall x:D, (exists y, R x y) -> R x x.
1 subgoal
D : Set
R : D -> D -> Prop
R_symmetric : forall x y : D, R x y -> R y x
R_transitive : forall x y z : D, R x y -> R y z -> R x z
============================
forall x : D, (exists y : D, R x y) -> R x x
refl_if < Check ex.
ex
: forall A : Type, (A -> Prop) -> Prop
refl_if < intros x x_Rlinked.
1 subgoal
D : Set
R : D -> D -> Prop
R_symmetric : forall x y : D, R x y -> R y x
R_transitive : forall x y z : D, R x y -> R y z -> R x z
x : D
x_Rlinked : exists y : D, R x y
============================
R x x
refl_if < intro y.
Toplevel input, characters 0-7
> intro y.
> ^^^^^^^
User error: No product even after head-reduction
refl_if <
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