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Proof step 13 from proof getarray-addarray-02 (previous step)

0 ≤ i ⊦ getarray(r, 0, i, addarray(r, intval(0), i, st[r -- _type, typeval(mkarraytype(int_type))])[r -- _length, intval(i)]) = mklist(intval(0), i→n(i))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ is_fskey(sk) ∨ r ≠ r0 → addarray(r, val, i, st[r0 -- sk, val0]) = (addarray(r, val, i, st)[r0 -- sk, val0])
Proof step 12:
is_fskey(_type) ∨ r ≠ r, 0 ≤ i ⊦ getarray(r, 0, i, addarray(r, intval(0), i, st)[r -- _type, typeval(mkarraytype(int_type))][r -- _length, intval(i)]) = mklist(intval(0), i→n(i))

Rule argument

[crewrite-arg: add-put-switch , F , [val0, sk, r0, st, i, val, r] → [typeval(mkarraytype(int_type)), _type, r, st, i, intval(0), r] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_fskey(_type)])], [EXTRATERMS : (typeval(mkarraytype(int_type)), _type, r, st, i, intval(0), r)]]