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Proof step 18 from proof isarray-put-field (previous step)

st[r -- _type] = typeval(mkarraytype(ty)) ⊦ fs ' = _length, fs ' = _type, r -- _type ∈ st[r0 -- fs ', val] ∧ okreftype(refval(r), mkarraytype(ty), st[r0 -- fs ', val]) ∧ r ≠ jvmref ∧ r -- _length ∈ st[r0 -- fs ', val] ∧ is_integervalue(st[r0 -- fs ', val][r -- _length]) ∧ 0 ≤ (st[r0 -- fs ', val][r -- _length]) .intval ∧ is_arrayref(r, (st[r0 -- fs ', val][r -- _length]) .intval, st[r0 -- fs ', val]) ∧ (∀ j. 0 ≤ j ∧ j < (st[r0 -- fs ', val][r -- _length]) .intval → oktype(st[r0 -- fs ', val][r -- j '], ty, st[r0 -- fs ', val])) ↔ r -- _type ∈ st ∧ okarray(r, ty, st), r = jvmref

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ 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 5:
⊦ sk0 ≠ _type → (oktype(val, ty, st[r -- sk0, val0]) ↔ oktype(val, ty, st))
Proof step 6:
⊦ oktype(val, ty, st) ↔ okval(val, ty)
Proof step 17:
st[r -- _type] = typeval(mkarraytype(ty)) ⊦ r = jvmref, fs ' = _length, fs ' = _type, r -- _type ∈ st[r0 -- fs ', val] ∧ is_typevalue(typeval(mkarraytype(ty))) ∧ is_arraytype(typeval(mkarraytype(ty)) .type) ∧ typeval(mkarraytype(ty)) .type .type ≤ ty ∧ r -- _length ∈ st[r0 -- fs ', val] ∧ is_integervalue(st[r -- _length]) ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ (∀ j. ¬ j < 0 ∧ ¬ st[r -- _length] .intval ≤ j → okval(st[r -- j '], ty)) ↔ r -- _type ∈ st ∧ okarray(r, ty, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (st[r0 -- fs ', val][r -- i ']) = st[r -- i ']], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ is_arrayref (r, i, st[r0 -- fs ', val]) ↔ is_arrayref(r, i, st)], [CSIMPSEQ : ⊦ ty0 ≤ mkarraytype(ty) ↔ is_arraytype(ty0) ∧ ty0 .type ≤ ty], [CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))])]]