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Induction

This is the task corresponding to exercise 1. Induction.

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Definitions File 

theory Defs
  imports "HOL-IMP.AExp"
begin

fun right2 :: "aexp \<Rightarrow> aexp \<Rightarrow> aexp" where
"right2 (V x) a = Plus (V x) a" |
"right2 (N i) a = Plus (N i) a" |
"right2 (Plus a1 a2) a = right2 a1 (right2 a2 a)"

definition right :: "aexp \<Rightarrow> aexp" where
"right a = right2 a (N 0)"

end

Template File 

theory Submission
  imports Defs
begin

theorem aval_right: "aval (right a) s = aval a s"
  sorry

end

Check File 

theory Check
  imports Submission
begin

lemma "aval (right a) s = aval a s"
  by (rule Submission.aval_right)

end
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