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Clean-up in example 2

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Patrick Lühne 2020-05-28 18:40:33 +02:00
parent c05eb11855
commit 7895bf83c4
Signed by: patrick
GPG Key ID: 05F3611E97A70ABF
1 changed files with 0 additions and 9 deletions
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examples/example-2.spec
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@ -19,12 +19,6 @@ axiom: forall N1, N2, N3 (N1 > N2 and N3 > 0 -> N1 * N3 > N2 * N3).
axiom: forall N1 (p(N1) and forall N2 (N2 >= N1 and not p(N2) -> not p(N2 + 1)) -> forall N2 (N2 >= N1 -> p(N2))).
#axiom: p(0) and forall N (N >= 0 and p(N) -> p(N + 1)) -> forall N p(N).
#lemma(forward): forall N N * N >= N.
#lemma(forward): forall X (q(X) -> exists N X = N).
#lemma(forward): forall X (q(X) <-> exists N (X = N and N >= 0 and N * N <= n and not p(N + 1))).
#lemma(forward): exists N (q(N) <-> N >= 0 and N * N <= n and (N + 1) * (N + 1) > n).
#lemma(forward): exists N p(N).
#lemma(forward): forall N1, N2 (N2 > N1 and N1 >= 0 and p(N2) -> p(N1)).
lemma(forward): forall X (p(X) <-> exists N (X = N and N >= 0 and N * N <= 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): forall N1, N2 (N1 >= 0 and N2 >= 0 and N1 < N2 -> N1 * N1 < N2 * N2).
@ -35,8 +29,5 @@ lemma(forward): forall N (N >= 0 and not p(N + 1) -> (N + 1) * (N + 1) > n).
lemma(backward): forall N1, N2 (q(N1) and q(N2) -> N1 = N2).
axiom: forall N1, N2 (p(N1) and not p(N1 + 1) and p(N2) and not p(N2 + 1) -> N1 = N2).
#lemma(backward): exists N (p(N) and not p(N + 1)).
#axiom: forall N (not p(N) -> not p(N + 1)).
lemma(backward): forall X1 (q(X1) -> p(X1) and exists X2 (exists N (X2 = N + 1 and N = X1) and not p(X2))).
#lemma(backward): forall X1 (q(X1) <- p(X1) and exists X2 (exists N (X2 = N + 1 and N = X1) and not p(X2))).