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Diffstat (limited to 'test-suite/success/Injection.v')
| -rw-r--r-- | test-suite/success/Injection.v | 34 |
1 files changed, 34 insertions, 0 deletions
diff --git a/test-suite/success/Injection.v b/test-suite/success/Injection.v new file mode 100644 index 00000000..fd80cec6 --- /dev/null +++ b/test-suite/success/Injection.v @@ -0,0 +1,34 @@ +(* Check the behaviour of Injection *) + +(* Check that Injection tries Intro until *) + +Lemma l1 : (x:nat)(S x)=(S (S x))->False. +Injection 1. +Apply n_Sn. +Qed. + +Lemma l2 : (x:nat)(H:(S x)=(S (S x)))H==H->False. +Injection H. +Intros. +Apply (n_Sn x H0). +Qed. + +(* Check that no tuple needs to be built *) +Lemma l3 : (x,y:nat) + (existS ? [n:nat]({n=n}+{n=n}) x (left ? ? (refl_equal nat x)))= + (existS ? [n:nat]({n=n}+{n=n}) y (left ? ? (refl_equal nat y))) + -> x=y. +Intros x y H. +Injection H. +Exact [H]H. +Qed. + +(* Check that a tuple is built (actually the same as the initial one) *) +Lemma l4 : (p1,p2:{O=O}+{O=O}) + (existS ? [n:nat]({n=n}+{n=n}) O p1)=(existS ? [n:nat]({n=n}+{n=n}) O p2) + ->(existS ? [n:nat]({n=n}+{n=n}) O p1)=(existS ? [n:nat]({n=n}+{n=n}) O p2). +Intros. +Injection H. +Exact [H]H. +Qed. + |