equal
deleted
inserted
replaced
75 done |
75 done |
76 |
76 |
77 lemma increasingD2: "[| f \<in> increasing(A); x<=A |] ==> x <= f`x" |
77 lemma increasingD2: "[| f \<in> increasing(A); x<=A |] ==> x <= f`x" |
78 by (unfold increasing_def, blast) |
78 by (unfold increasing_def, blast) |
79 |
79 |
80 lemmas TFin_UnionI = PowI [THEN TFin.Pow_UnionI, standard] |
80 lemmas TFin_UnionI = PowI [THEN TFin.Pow_UnionI] |
81 |
81 |
82 lemmas TFin_is_subset = TFin.dom_subset [THEN subsetD, THEN PowD, standard] |
82 lemmas TFin_is_subset = TFin.dom_subset [THEN subsetD, THEN PowD] |
83 |
83 |
84 |
84 |
85 text{*Structural induction on @{term "TFin(S,next)"} *} |
85 text{*Structural induction on @{term "TFin(S,next)"} *} |
86 lemma TFin_induct: |
86 lemma TFin_induct: |
87 "[| n \<in> TFin(S,next); |
87 "[| n \<in> TFin(S,next); |