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Proof step 17 from proof isarray-put (previous step)

st[r1 -- _type] = typeval(mkarraytype(ty0)), st[r1 -- _length] = intval(i), 0 ≤ i, r1 -- _length ∈ st, is_arrayref(r1, i, st), r1 -- _type ∈ st, r1 ∈ st, okval(val, ty), ∀ j0. ¬ j0 < 0 ∧ ¬ i ≤ j0 → okval(st[r1 -- j0 '], ty0) ⊦ ty = void_type, mkfs(class, ty, fieldvar) ' = _length, r1 = jvmref, okreftype(refval(r1), mkarraytype(ty0), st[r1 -- mkfs(class, ty, fieldvar) ', val]) ∧ (0 ≤ j ∧ j < i → okval(st[r1 -- j '], ty0))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ okreftype(val, ty, st) ↔ is_referencevalue(val) ∧ (val .refval ≠ jvmref → val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type ≤ ty)
Proof step 16:
st[r1 -- _type] = typeval(mkarraytype(ty0)), st[r1 -- _length] = intval(i), 0 ≤ i, r1 -- _length ∈ st, is_arrayref(r1, i, st), r1 -- _type ∈ st, r1 ∈ st, okval(val, ty), ∀ j0. ¬ j0 < 0 ∧ ¬ i ≤ j0 → okval(st[r1 -- j0 '], ty0) ⊦ ty = void_type, mkfs(class, ty, fieldvar) ' = _length, r1 = jvmref, is_referencevalue(refval(r1)) ∧ ( refval(r1) .refval ≠ jvmref → refval(r1) .refval -- _type ∈ st[r1 -- mkfs(class, ty, fieldvar) ', val] ∧ is_typevalue(st[r1 -- mkfs(class, ty, fieldvar) ', val][refval(r1) .refval -- _type]) ∧ (st[r1 -- mkfs(class, ty, fieldvar) ', val][refval(r1) .refval -- _type]) .type ≤ mkarraytype(ty0)) ∧ (0 ≤ j ∧ j < i → okval(st[r1 -- j '], ty0))

Rule argument

[crewrite-arg: okreftype , F , [st, ty, val] → [st[r1 -- mkfs(class, ty, fieldvar) ', val], mkarraytype(ty0), refval(r1)] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r1 -- mkfs(class, ty, fieldvar) ', val], mkarraytype(ty0), refval(r1))]]