inductive finite_stp :: "('a => bool) => 'a set => bool"
where
stp_emptyI [simp, intro!]: "finite_stp Pa {}" |
stp_insertI[simp, intro!]: "finite_stp Pa A /\ Pa a ==>
finite_stp Pa (insert a A)"
lemma stp_finite_induct [case_names empty insert, induct set: finite_stp]:
"finite_stp Pa F /\ Pa x ==>
P {} ==> (!!x Pa F . finite_stp Pa F ==> x ∉ F ==>
P F ==> P (insert x F))
==> P F"
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