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# Homework 10

This is the task corresponding to homework 10.

## Resources

### Definitions File

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

definition "SQUARE \<equiv>
''z'' ::= N 1;;
''a'' ::= N 0;;
WHILE Less (N 0) (V ''n'') DO (
''a'' ::= Plus (V ''a'') (V ''z'');;
''z'' ::= Plus (V ''z'') (N 2);;
''n'' ::= Plus (V ''n'') (N (-1))
)"

bundle ACOM begin
no_notation SKIP ("SKIP")
no_notation Assign ("_ ::= _" [1000, 61] 61)
no_notation Seq    ("_;;/ _"  [60, 61] 60)
no_notation If ("(IF _/ THEN _/ ELSE _)"  [0, 0, 61] 61)
notation Aassign ("(_ ::= _)" [1000, 61] 61)
notation Aseq ("_;;/ _"  [60, 61] 60)
notation Aif ("(IF _/ THEN _/ ELSE _)"  [0, 0, 61] 61)
end

bundle COM begin
no_notation Aassign ("(_ ::= _)" [1000, 61] 61)
no_notation Aseq ("_;;/ _"  [60, 61] 60)
no_notation Aif ("(IF _/ THEN _/ ELSE _)"  [0, 0, 61] 61)
notation SKIP ("SKIP")
notation Assign ("_ ::= _" [1000, 61] 61)
notation Seq    ("_;;/ _"  [60, 61] 60)
notation If ("(IF _/ THEN _/ ELSE _)"  [0, 0, 61] 61)
end

unbundle COM

end```

### Template File

```theory Submission
imports Defs
begin

theorem SQUARE_correct:
"\<turnstile> {\<lambda>s. s ''n'' \<ge> 0 \<and> s=s\<^sub>0} SQUARE {\<lambda>s. s ''a'' = s\<^sub>0 ''n'' * s\<^sub>0 ''n''}"
sorry

end```

### Check File

```theory Check
imports Submission
begin

theorem SQUARE_correct: "\<turnstile> {\<lambda>s. s ''n'' \<ge> 0 \<and> s=s\<^sub>0} SQUARE {\<lambda>s. s ''a'' = s\<^sub>0 ''n'' * s\<^sub>0 ''n''}"
by (rule Submission.SQUARE_correct)

end```

Terms and Conditions