Require Import TestSuite.admit. (* File reduced by coq-bug-finder from original input, then from 12178 lines to 457 lines, then from 500 lines to 147 lines, then from 175 lines to 56 lines *) (* coqc version trunk (September 2014) compiled on Sep 21 2014 16:34:4 with OCaml 4.01.0 coqtop version cagnode16:/afs/csail.mit.edu/u/j/jgross/coq-trunk,trunk (eaf864354c3fda9ddc1f03f0b1c7807b6fd44322) *) Axiom transport : forall {A : Type} (P : A -> Type) {x y : A} (p : x = y) (u : P x), P y. Axiom ap : forall {A B:Type} (f:A -> B) {x y:A} (p:x = y), f x = f y. Module NonPrim. Class Contr_internal (A : Type) := { center : A ; contr : (forall y : A, center = y) }. Arguments center A {_} / . Inductive trunc_index : Type := minus_two | trunc_S (_ : trunc_index). Notation "-2" := minus_two (at level 0). Fixpoint IsTrunc_internal (n : trunc_index) (A : Type) : Type := match n with | -2 => Contr_internal A | trunc_S n' => forall (x y : A), IsTrunc_internal n' (x = y) end. Class IsTrunc (n : trunc_index) (A : Type) : Type := Trunc_is_trunc : IsTrunc_internal n A. Notation Contr := (IsTrunc -2). Hint Extern 0 => progress change Contr_internal with Contr in * : typeclass_instances. Goal forall (H : Type) (H0 : H -> H -> Type) (H1 : Type) (H2 : Contr H1) (H3 : H1) (H4 : H1 -> H) (H5 : H0 (H4 (center H1)) (H4 H3)) (H6 : H0 (H4 (center H1)) (H4 (center H1))), transport (fun y : H => H0 (H4 (center H1)) y) (ap H4 (contr H3)) H6 = H5. intros. match goal with | [ |- context[contr (center _)] ] => fail 1 "bad" | _ => idtac end. match goal with | [ H : _ |- _ ] => destruct (contr H) end. match goal with | [ |- context[contr (center ?x)] ] => fail 1 "bad" x | _ => idtac end. admit. Defined. End NonPrim. Module Prim. Set Primitive Projections. Class Contr_internal (A : Type) := { center : A ; contr : (forall y : A, center = y) }. Arguments center A {_} / . Inductive trunc_index : Type := minus_two | trunc_S (_ : trunc_index). Notation "-2" := minus_two (at level 0). Fixpoint IsTrunc_internal (n : trunc_index) (A : Type) : Type := match n with | -2 => Contr_internal A | trunc_S n' => forall (x y : A), IsTrunc_internal n' (x = y) end. Class IsTrunc (n : trunc_index) (A : Type) : Type := Trunc_is_trunc : IsTrunc_internal n A. Notation Contr := (IsTrunc -2). Hint Extern 0 => progress change Contr_internal with Contr in * : typeclass_instances. Goal forall (H : Type) (H0 : H -> H -> Type) (H1 : Type) (H2 : Contr H1) (H3 : H1) (H4 : H1 -> H) (H5 : H0 (H4 (center H1)) (H4 H3)) (H6 : H0 (H4 (center H1)) (H4 (center H1))), transport (fun y : H => H0 (H4 (center H1)) y) (ap H4 (contr H3)) H6 = H5. intros. match goal with | [ |- context[contr (center _)] ] => fail 1 "bad" | _ => idtac end. match goal with | [ H : _ |- _ ] => destruct (contr H) end. match goal with | [ |- context[contr (center ?x)] ] => fail 1 "bad" x | _ => idtac end. (* Error: Tactic failure: bad H1. *) admit. Defined. End Prim.