wenzelm@58889: section {* Example 3.8 *}
wenzelm@4905: 
wenzelm@17248: theory Ex2
wenzelm@17248: imports LCF
wenzelm@17248: begin
wenzelm@4905: 
wenzelm@47025: axiomatization
wenzelm@47025:   P     :: "'a => tr" and
wenzelm@47025:   F     :: "'b => 'b" and
wenzelm@47025:   G     :: "'a => 'a" and
wenzelm@47025:   H     :: "'a => 'b => 'b" and
wenzelm@17248:   K     :: "('a => 'b => 'b) => ('a => 'b => 'b)"
wenzelm@47025: where
wenzelm@47025:   F_strict:     "F(UU) = UU" and
wenzelm@47025:   K:            "K = (%h x y. P(x) => y | F(h(G(x),y)))" and
wenzelm@17248:   H:            "H = FIX(K)"
wenzelm@17248: 
wenzelm@19755: declare F_strict [simp] K [simp]
wenzelm@19755: 
wenzelm@19755: lemma example: "ALL x. F(H(x::'a,y::'b)) = H(x,F(y))"
wenzelm@19755:   apply (simplesubst H)
wenzelm@27208:   apply (tactic {* induct_tac @{context} "K:: ('a=>'b=>'b) => ('a=>'b=>'b)" 1 *})
wenzelm@47025:   apply simp
wenzelm@47025:   apply (simp split: COND_cases_iff)
wenzelm@19755:   done
wenzelm@4905: 
wenzelm@4905: end