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theory Defs imports Main begin end
theory Submission
imports Defs
begin
lemma induct_pcpl:
"\<lbrakk>P []; \<And>x. P [x]; \<And>x y zs. P zs \<Longrightarrow> P (x # y # zs)\<rbrakk> \<Longrightarrow> P xs"
by induction_schema (pat_completeness, lexicographic_order)
lemma split_splice:
"\<exists>ys zs. xs = splice ys zs \<and> length ys \<ge> (length xs) div 2 \<and> length zs \<ge> (length xs) div 2"
proof(induction xs rule: induct_pcpl)
case 1
show ?case
sorry
next
case (2 x)
show ?case
sorry
next
case (3 y z xs)
show ?case
sorry
qed
lemma eq_identiy:
fixes f :: "nat \<Rightarrow> nat"
assumes "\<forall>n. f(Suc n) = f(n)^2"
shows "f(n) = f(0)^(2^n)"
sorry
end
theory Check imports Submission begin lemma split_splice: "\<exists>ys zs. xs = splice ys zs \<and> length ys \<ge> (length xs) div 2 \<and> length zs \<ge> (length xs) div 2" by(rule split_splice) lemma eq_identiy: fixes f :: "nat \<Rightarrow> nat" assumes "\<forall>n. f(Suc n) = f(n)^2" shows "f(n) = f(0)^(2^n)" by(rule eq_identiy[OF assms]) end