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Proof step 39 from proof okarray-init-04 (previous step)

⊦ r = jvmref, (∀ j. ¬ j < 0 ∧ ¬ n→i(# vals) < j → is_bytevalue(addarray(r, byte_type, vals + byteval(by) ', st)[r -- j '])) ↔ is_arrayref(r, n→i(# vals), addarray(r, byte_type, vals, st)) ∧ (∀ j. 0 ≤ j ∧ j < n→i(# vals) → is_bytevalue(vals[i→n(j)]))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ i ≤ n→i(# vals) → is_arrayref(r, i, addarray(r, ty, vals, st))
Proof step 38:
n→i(# vals) ≤ n→i(# vals) ⊦ r = jvmref, (∀ j. ¬ j < 0 ∧ ¬ n→i(# vals) < j → is_bytevalue(addarray(r, byte_type, vals + byteval(by) ', st)[r -- j '])) ↔ true ∧ (∀ j. 0 ≤ j ∧ j < n→i(# vals) → is_bytevalue(vals[i→n(j)]))

Rule argument

[crewrite-arg: isarray-init-02 , F , [st, vals, ty, i, r] → [st, vals, byte_type, n→i(# vals), r] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ n→i(m) ≤ n→i(n) ↔ m ≤ n], [CSIMPSEQ : ⊦ ¬ m ≤ n ↔ n < m], [CSIMPSEQ : ⊦ ¬ n < n])], [EXTRATERMS : (st, vals, byte_type, n→i(# vals), r)]]