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Patrick Lühne
2020-05-07 17:19:42 +02:00
parent 5469f7d7b2
commit 753cc3e5a8
3 changed files with 93 additions and 21 deletions
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9
examples/example-2.spec
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@@ -1,9 +1,8 @@
axiom: forall N1, N2, N3 (N1 > N2 and N3 > 0 -> N1 * N3 > N2 * N3).
axiom: p(0) and forall N (N >= 0 and p(N) -> p(N + 1)).
input: n -> integer.
axiom: forall N1, N2, N3 (N1 > N2 and N3 > 0 -> N1 * N3 > N2 * N3).
axiom: p(0) and forall N (N >= 0 and p(N) -> p(N + 1)).
assume: n >= 0.
assert: exists N (forall X (q(X) <-> X = N) and N >= 0 and N * N <= n and (N + 1) * (N + 1) > n).
@@ -16,6 +15,8 @@ lemma(forward): forall X (p(X) <-> exists N2 (X = N2 and N2 >= 0 and N2 * N2 <=
lemma(forward): forall X (q(X) <-> exists N2 (X = N2 and N2 >= 0 and N2 * N2 <= n and not p(N2 + 1))).
lemma(forward): forall N2 (N2 >= 0 and not p(N2 + 1) -> (N2 + 1) * (N2 + 1) > n).
lemma(forward): forall X (q(X) <-> exists N2 (X = N2 and N2 >= 0 and N2 * N2 <= n and (N2 + 1) * (N2 + 1) > n)).
lemma(forward): exists N2 (forall X (X = N2 -> (q(X) <-> N2 >= 0 and N2 * N2 <= n and (N2 + 1) * (N2 + 1) > n))).
lemma(forward): exists N2 p(N2).
lemma(forward): forall N1, N2 (N1 >= 0 and N2 >= 0 and N1 < N2 -> N1 * N1 < N2 * N2).