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Proof step 9 from proof exactarray-primput (previous step)

st[r -- _type] = typeval(mkarraytype(ty)), r ∈ st, is_arrayref(r, st[r -- _length] .intval, st), r -- _length ∈ st, r -- _type ∈ st, j < st[r -- _length] .intval, okprimtype(val, ty), 0 < st[r -- _length] .intval, 0 ≤ j ⊦ r = jvmref, exactreftype(refval(r), mkarraytype(ty), st[r -- j ', val]) ∧ refval(r) .refval ≠ jvmref ∧ (refval(r) .refval -- _length) × intval(st[r -- _length] .intval) ∈ st[r -- j ', val] ∧ is_arrayref(refval(r) .refval, st[r -- _length] .intval, st[r -- j ', val])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
⊦ exactreftype(val, ty, st) ↔ is_referencevalue(val) ∧ val .refval ∈ st ∧ (val .refval ≠ jvmref → val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type = ty)
Proof step 8:
st[r -- _type] = typeval(mkarraytype(ty)), r ∈ st, is_arrayref(r, st[r -- _length] .intval, st), r -- _length ∈ st, r -- _type ∈ st, j < st[r -- _length] .intval, okprimtype(val, ty), 0 < st[r -- _length] .intval, 0 ≤ j ⊦ r = jvmref, exactreftype(refval(r), mkarraytype(ty), st[r -- j ', val])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_arrayref(r, i, st) → is_arrayref (r, i, st[r -- j ', val])], [CSIMPSEQ : ⊦ (st[r -- i ', val][r0 -- _length] ) = st[r0 -- _length]], [CSIMPSEQ : sk ≠ sk0 ⊦ r -- sk ∈ st[r -- sk0, val] ↔ r -- sk ∈ st], [CSIMPSEQ : ⊦ _length ≠ i '], [CSIMPSEQ : ⊦ rk × val ∈ st ↔ ¬ ¬ (rk ∈ st ∧ st[rk] = val)], [CSIMPSEQ : is_integervalue(val) ⊦ intval(val .intval) = val], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ r ∈ st[r -- sk, val]], [CSIMPSEQ : ⊦ r -- _type ∈ st[r0 -- i ', val0] ↔ r -- _type ∈ st], [CSIMPSEQ : ⊦ (st[r -- i ', val][r0 -- _type]) = st[r0 -- _type]], [CSIMPSEQ : ⊦ i ≤ j → ( is_arrayref (r, i, st[r0 -- j ', val]) ↔ is_arrayref(r, i, st))], [CSIMPSEQ : ⊦ ¬ is_integervalue(val) → val .intval = 0], [CSIMPSEQ : ⊦ refval(r) .refval = r])]]