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417 lemmas GreatestM_natI = GreatestM_nat_lemma [THEN conjunct1, standard] |
417 lemmas GreatestM_natI = GreatestM_nat_lemma [THEN conjunct1, standard] |
418 |
418 |
419 lemma GreatestM_nat_le: |
419 lemma GreatestM_nat_le: |
420 "P x ==> \<forall>y. P y --> m y < b |
420 "P x ==> \<forall>y. P y --> m y < b |
421 ==> (m x::nat) <= m (GreatestM m P)" |
421 ==> (m x::nat) <= m (GreatestM m P)" |
422 apply (blast dest: GreatestM_nat_lemma [THEN conjunct2, THEN spec]) |
422 apply (blast dest: GreatestM_nat_lemma [THEN conjunct2, THEN spec, of P]) |
423 done |
423 done |
424 |
424 |
425 |
425 |
426 text {* \medskip Specialization to @{text GREATEST}. *} |
426 text {* \medskip Specialization to @{text GREATEST}. *} |
427 |
427 |