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Proof step 37 from proof okarray-subset (previous step)

st ⊆ st0, okreftype(refval(r), mkarraytype(ty), st) ∧ refval(r) .refval ≠ jvmref ∧ (refval(r) .refval -- _length) × intval(st[r -- _length] .intval) ∈ st ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(refval(r) .refval, st[r -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r -- _length] .intval → oktype(st[refval(r) .refval -- j '], ty, st)) ⊦ r = jvmref, (0 ≤ j ∧ j < st[r -- _length] .intval → okval(st0[r -- j '], ty)) ∧ is_arrayref(r, st[r -- _length] .intval, st0) ∧ ¬ st[r -- _length] .intval < 0 ∧ st0[r -- _length] = intval(st[r -- _length] .intval) ∧ r -- _length ∈ st0 ∧ okreftype(refval(r), mkarraytype(ty), st0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
⊦ 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 8:
⊦ oktype(val, ty, st) ↔ okval(val, ty)
Proof step 36:
st[r -- _length] = intval(st[r -- _length] .intval), r ∈ st0, 0 ≤ st[r -- _length] .intval, r ∈ st, r -- _length ∈ st0, is_arrayref(r, st[r -- _length] .intval, st), r -- _length ∈ st, st[r -- _type] .type .type ≤ ty, is_arraytype(st[r -- _type] .type), is_typevalue(st[r -- _type]), r -- _type ∈ st, st ⊆ st0, ∀ j0. ¬ j0 < 0 ∧ ¬ st[r -- _length] .intval ≤ j0 → okval(st[r -- j0 '], ty) ⊦ r = jvmref, okreftype(refval(r), mkarraytype(ty), st0) ∧ is_arrayref(r, st[r -- _length] .intval, st0) ∧ (0 ≤ j ∧ j < st[r -- _length] .intval → okval(st0[r -- j '], ty))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ rk ∈ st ∧ st ⊆ st1 → (st[rk] ≠ st1[rk] ↔ false)], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ rk ∈ st ∧ ¬ rk ∈ st0 → ¬ st ⊆ st0], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ rk × val ∈ st ↔ rk ∈ st ∧ st[rk] = val], [CSIMPSEQ : ⊦ ty0 ≤ mkarraytype(ty) ↔ is_arraytype(ty0) ∧ ty0 .type ≤ ty], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ refval(r) .refval = r])]]