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-rw-r--r--Test/dafny1/MoreInduction.dfy14
1 files changed, 7 insertions, 7 deletions
diff --git a/Test/dafny1/MoreInduction.dfy b/Test/dafny1/MoreInduction.dfy
index 41adcf50..319bb8d0 100644
--- a/Test/dafny1/MoreInduction.dfy
+++ b/Test/dafny1/MoreInduction.dfy
@@ -42,13 +42,13 @@ function ToSeq<X>(list: List<X>): seq<X>
case Nary(nn) => ToSeq(nn) + ToSeq(rest)
}
-ghost method Theorem<X>(list: List<X>)
+lemma Theorem<X>(list: List<X>)
ensures ToSeq(list) == ToSeq(FlattenMain(list));
{
Lemma(list, Nil);
}
-ghost method Lemma<X>(list: List<X>, ext: List<X>)
+lemma Lemma<X>(list: List<X>, ext: List<X>)
requires IsFlat(ext);
ensures ToSeq(list) + ToSeq(ext) == ToSeq(Flatten(list, ext));
{
@@ -73,27 +73,27 @@ function NegFac(n: int): int
if -1 <= n then -1 else - NegFac(n+1) * n
}
-ghost method LemmaAll()
+lemma LemmaAll()
ensures forall n :: NegFac(n) <= -1; // error: induction heuristic does not give a useful well-founded order, and thus this fails to verify
{
}
-ghost method LemmaOne(n: int)
+lemma LemmaOne(n: int)
ensures NegFac(n) <= -1; // error: induction heuristic does not give a useful well-founded order, and thus this fails to verify
{
}
-ghost method LemmaAll_Neg()
+lemma LemmaAll_Neg()
ensures forall n :: NegFac(-n) <= -1; // error: fails to verify because of the minus in the trigger
{
}
-ghost method LemmaOne_Neg(n: int)
+lemma LemmaOne_Neg(n: int)
ensures NegFac(-n) <= -1; // error: fails to verify because of the minus in the trigger
{
}
-ghost method LemmaOneWithDecreases(n: int)
+lemma LemmaOneWithDecreases(n: int)
ensures NegFac(n) <= -1; // here, the programmer gives a good well-founded order, so this verifies
decreases -n;
{