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authorGravatar Jason Gross <jgross@mit.edu>2014-05-06 09:51:21 -0400
committerGravatar Jason Gross <jgross@mit.edu>2014-05-06 16:11:43 -0400
commitd1a39e06c44dc451d8a56a286017885d400ac435 (patch)
treef83237ecf03b9d809d888ea31a842e6fb6d716d0 /test-suite/bugs/closed/HoTT_coq_047.v
parentd40091c015b68cc1a8403ca5dcc74323bf939f37 (diff)
Add regression tests for univ. poly. and prim proj
These regression tests are aggregated from the various bugs I (and others) have reported on https://github.com/HoTT/coq/issues relating to universe polymorphism, primitive projections, and eta for records. These are the tests that trunk currently passes. I'm not sure about the naming scheme (HoTT_coq_###.v, where ### is the number of the issue in GitHub), but I couldn't think of a better one.
Diffstat (limited to 'test-suite/bugs/closed/HoTT_coq_047.v')
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diff --git a/test-suite/bugs/closed/HoTT_coq_047.v b/test-suite/bugs/closed/HoTT_coq_047.v
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+++ b/test-suite/bugs/closed/HoTT_coq_047.v
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+Inductive nCk : nat -> nat -> Type :=
+ |zz : nCk 0 0
+ | incl { m n : nat } : nCk m n -> nCk (S m) (S n)
+ | excl { m n : nat } : nCk m n -> nCk (S m) n.
+
+Definition nCkComp { l m n : nat } :
+ nCk l m -> nCk m n -> nCk l n.
+Proof.
+ intro.
+ revert n.
+ induction H.
+ auto.
+(* ( incl w ) o zz -> contradiction *)
+ intros.
+ remember (S n) as sn.
+ destruct H0.
+ discriminate Heqsn.
+ apply incl.
+ apply IHnCk.
+ injection Heqsn.
+ intro.
+ rewrite <- H1.
+ auto.
+ apply excl.
+ apply IHnCk.
+ injection Heqsn.
+ intro. rewrite <- H1.
+ auto.
+ intros.
+ apply excl.
+ apply IHnCk.
+ auto.
+Defined.
+
+Lemma nCkEq { k l m n : nat } ( cs : nCk k l ) (ct : nCk l m) (cr : nCk m n ):
+ nCkComp cs (nCkComp ct cr) = nCkComp (nCkComp cs ct) cr.
+Proof.
+ revert m n ct cr.
+ induction cs.
+ intros. simpl. auto.
+ intros.
+ destruct n.
+ destruct m0.
+ destruct n0.
+ destruct cr.
+(* Anomaly: Evar ?nnn was not declared. Please report. *)