diff options
| -rw-r--r-- | hott/Identity.thy | 4 | ||||
| -rw-r--r-- | hott/Nat.thy | 2 |
2 files changed, 3 insertions, 3 deletions
diff --git a/hott/Identity.thy b/hott/Identity.thy index 8675134..308e664 100644 --- a/hott/Identity.thy +++ b/hott/Identity.thy @@ -473,7 +473,7 @@ Lemma (derive) right_whisker: have "t \<bullet> refl x = t" by (rule pathcomp_refl) also have ".. = s" by fact also have ".. = s \<bullet> refl x" by (rule pathcomp_refl[symmetric]) - finally show "t \<bullet> refl x = s \<bullet> refl x" by this + finally show "{}" by this qed done @@ -486,7 +486,7 @@ Lemma (derive) left_whisker: have "refl x \<bullet> t = t" by (rule refl_pathcomp) also have ".. = s" by fact also have ".. = refl x \<bullet> s" by (rule refl_pathcomp[symmetric]) - finally show "refl x \<bullet> t = refl x \<bullet> s" by this + finally show "{}" by this qed done diff --git a/hott/Nat.thy b/hott/Nat.thy index 22c1860..50b7996 100644 --- a/hott/Nat.thy +++ b/hott/Nat.thy @@ -151,7 +151,7 @@ Lemma (derive) zero_mul: proof reduce have "0 + 0 * n = 0 + 0 " by (eq ih) refl also have ".. = 0" by reduce refl - finally show "0 + 0 * n = 0" by this + finally show "{}" by this qed done |