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 < |