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# Big-Step Semantics

This is the task corresponding to exercise 2. Big-Step Semantics.

## Resources

### Definitions File

```theory Defs
imports "HOL-IMP.Big_Step"
begin

declare [[names_short]]
declare assign_simp[simp]

consts sim_if :: "vname \<Rightarrow> bexp \<Rightarrow> com \<Rightarrow> com"

end
```

### Template File

```theory Submission
imports Defs
begin

definition sim_if :: "vname \<Rightarrow> bexp \<Rightarrow> com \<Rightarrow> com" where
"sim_if _ = undefined"

theorem sim_if_sound:
assumes step: "(IF b THEN SKIP ELSE c, s) \<Rightarrow> t"
and zero: "s x = 0" "t x = 0"
shows "(sim_if x b c, s) \<Rightarrow> t"
sorry

end
```

### Check File

```theory Check
imports Submission
begin

lemma "\<lbrakk>(IF b THEN SKIP ELSE c, s) \<Rightarrow> t; s x = 0; t x = 0\<rbrakk> \<Longrightarrow> (sim_if x b c, s) \<Rightarrow> t"
by (rule Submission.sim_if_sound)

end
```

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