equal
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replaced
672 (* holds also in other direction, then equal to forallPfilterP *) |
672 (* holds also in other direction, then equal to forallPfilterP *) |
673 goal thy "Forall P x --> Filter P`x = x"; |
673 goal thy "Forall P x --> Filter P`x = x"; |
674 by (Seq_induct_tac "x" [Forall_def,sforall_def,Filter_def] 1); |
674 by (Seq_induct_tac "x" [Forall_def,sforall_def,Filter_def] 1); |
675 qed"ForallPFilterPid1"; |
675 qed"ForallPFilterPid1"; |
676 |
676 |
677 bind_thm(" ForallPFilterPid",ForallPFilterPid1 RS mp); |
677 bind_thm("ForallPFilterPid",ForallPFilterPid1 RS mp); |
678 |
678 |
679 |
679 |
680 (* holds also in other direction *) |
680 (* holds also in other direction *) |
681 goal thy "!! ys . Finite ys ==> \ |
681 goal thy "!! ys . Finite ys ==> \ |
682 \ Forall (%x. ~P x) ys --> Filter P`ys = nil "; |
682 \ Forall (%x. ~P x) ys --> Filter P`ys = nil "; |