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# Induction

This is the task corresponding to exercise 1. Induction.

## Resources

Download Files

### 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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