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Proof step 16 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, 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))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
st[r1 -- _length] = intval(i), st[r1 -- _type] = typeval(mkarraytype(ty0)), okval(val, ty), r1 ∈ st, r1 -- _type ∈ st, is_arrayref(r1, i, st), r1 -- _length ∈ st, 0 ≤ i, j < i, 0 ≤ j, 0 < i, ∀ j0. ¬ j0 < 0 ∧ ¬ i ≤ j0 → okval(st[r1 -- j0 '], ty0) ⊦ r1 = jvmref, mkfs(class, ty, fieldvar) ' = _length, ty = void_type, okval(st[r1 -- j '], ty0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ ty ≤ ty], [CSIMPSEQ : ⊦ mkarraytype(ty) ≤ mkarraytype(ty0) ↔ ty ≤ ty0], [CSIMPSEQ : ⊦ typeval(ty) .type = ty], [CSIMPSEQ : ⊦ is_typevalue(typeval(ty))], [CSIMPSEQ : ⊦ ty ≠ void_type → (st[ r -- mkfs (class, ty, fieldvar) ', val] [r0 -- _type ] ) = st[r0 -- _type]], [CSIMPSEQ : sk ≠ sk0 ⊦ r -- sk ∈ st[r -- sk0, val] ↔ r -- sk ∈ st], [CSIMPSEQ : ⊦ ty ≠ void_type → mkfs(class, ty, fieldvar) ' ≠ _type], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))])]]