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Proof step 41 from proof okarray-substore (previous step)

st[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(ty0)), is_arrayref(r, i, st), st ⊆ st0, r -- _type ∈ st, ty0 ≤ ty, r -- _length ∈ st, 0 ≤ i, r ∈ st, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st[r -- j '], ty, st) ⊦ r = jvmref, okreftype(refval(r), mkarraytype(ty), st0) ∧ refval(r) .refval ≠ jvmref ∧ (refval(r) .refval -- _length) × intval(i) ∈ st0 ∧ 0 ≤ i ∧ is_arrayref(refval(r) .refval, i, st0) ∧ (∀ j. 0 ≤ j ∧ j < i → oktype(st0[refval(r) .refval -- j '], ty, st0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 40:
st[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(ty0)), is_arrayref(r, i, st), st ⊆ st0, r -- _type ∈ st, ty0 ≤ ty, r -- _length ∈ st, 0 ≤ i, r ∈ st, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st[r -- j '], ty, st) ⊦ r = jvmref, okreftype(refval(r), mkarraytype(ty), st0) ∧ r -- _length ∈ st0 ∧ st0[r -- _length] = intval(i) ∧ is_arrayref(r, i, st0) ∧ (0 ≤ j ∧ j < i → oktype(st0[r -- j '], ty, st0))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ rk × val ∈ st ↔ ¬ ¬ (rk ∈ st ∧ st[rk] = val)], [CSIMPSEQ : ⊦ refval(r) .refval = r])]]