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Proof step 17 from proof okarray-put-08 (previous step)

⊦ fs ' = _length, fs ' = _type, is_referencevalue(val) ∧ val .refval -- _type ∈ st[r -- fs ', val0] ∧ is_typevalue(st[val .refval -- _type]) ∧ is_arraytype(st[val .refval -- _type] .type) ∧ st[val .refval -- _type] .type .type ≤ ty ∧ val .refval ≠ jvmref ∧ val .refval -- _length ∈ st[r -- fs ', val0] ∧ st[val .refval -- _length] = intval(i) ∧ 0 ≤ i ∧ is_arrayref(val .refval, i, st) ∧ (∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[val .refval -- j '], ty)) ↔ okarray(val, ty, i, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ okarray(val, ty, i, st) ↔ okreftype(val, mkarraytype(ty), st) ∧ val .refval ≠ jvmref ∧ (val .refval -- _length) × intval(i) ∈ st ∧ 0 ≤ i ∧ is_arrayref(val .refval, i, st) ∧ (∀ j. 0 ≤ j ∧ j < i → oktype(st[val .refval -- j '], ty, st))
Proof step 16:
⊦ fs ' = _length, fs ' = _type, is_referencevalue(val) ∧ val .refval -- _type ∈ st[r -- fs ', val0] ∧ is_typevalue(st[val .refval -- _type]) ∧ is_arraytype(st[val .refval -- _type] .type) ∧ st[val .refval -- _type] .type .type ≤ ty ∧ val .refval ≠ jvmref ∧ val .refval -- _length ∈ st[r -- fs ', val0] ∧ st[val .refval -- _length] = intval(i) ∧ 0 ≤ i ∧ is_arrayref(val .refval, i, st) ∧ (∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[val .refval -- j '], ty)) ↔ okreftype(val, mkarraytype(ty), st) ∧ val .refval ≠ jvmref ∧ (val .refval -- _length) × intval(i) ∈ st ∧ 0 ≤ i ∧ is_arrayref(val .refval, i, st) ∧ (∀ j. 0 ≤ j ∧ j < i → oktype(st[val .refval -- j '], ty, st))

Rule argument

[crewrite-arg: okarrayOfLength , F , [st, i, ty, val] → [st, i, ty, val] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, i, ty, val)]]