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Proof step 26 from proof okarray-okarray-01 (previous step)

okarray(r, ty, st), r ∈ st ⊦ r = jvmref, 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))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
⊦ okarray(r, ty, st) → intval(st[r -- _length] .intval) = st[r -- _length]
Proof step 9:
⊦ okarray(r, ty, st) → ¬ st[r -- _length] .intval < 0
Proof step 10:
⊦ oktype(val, ty, st) ↔ okval(val, ty)
Proof step 25:
okarray(r, ty, st), r ∈ st ⊦ r = jvmref, okreftype(refval(r), mkarraytype(ty), st) ∧ r -- _length ∈ st ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ (0 ≤ j ∧ j < st[r -- _length] .intval → okval(st[r -- j '], ty))

Rule argument

[emptyarg]

Additional information

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