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131 |
131 |
132 lemma wf_iff_acyclic_if_finite: "finite r ==> wf r = acyclic r" |
132 lemma wf_iff_acyclic_if_finite: "finite r ==> wf r = acyclic r" |
133 by (blast intro: finite_acyclic_wf wf_acyclic) |
133 by (blast intro: finite_acyclic_wf wf_acyclic) |
134 |
134 |
135 |
135 |
136 subsubsection{*Wellfoundedness of same\_fst*} |
136 subsubsection{*Wellfoundedness of @{term same_fst}*} |
137 |
137 |
138 lemma same_fstI [intro!]: |
138 lemma same_fstI [intro!]: |
139 "[| P x; (y',y) : R x |] ==> ((x,y'),(x,y)) : same_fst P R" |
139 "[| P x; (y',y) : R x |] ==> ((x,y'),(x,y)) : same_fst P R" |
140 by (simp add: same_fst_def) |
140 by (simp add: same_fst_def) |
141 |
141 |