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Proof step 12 from proof okarray-01 (previous step)

⊦ r = r0, okreftype(refval(r), mkarraytype(int_type), addarray(r0, ty0, i, st)) ∧ r ≠ jvmref ∧ r -- _length ∈ addarray(r0, ty0, i, st) ∧ is_integervalue(addarray(r0, ty0, i, st)[r -- _length]) ∧ 0 ≤ (addarray(r0, ty0, i, st)[r -- _length]) .intval ∧ is_arrayref(r, (addarray(r0, ty0, i, st)[r -- _length]) .intval, addarray(r0, ty0, i, st)) ∧ (∀ j. 0 ≤ j ∧ j < (addarray(r0, ty0, i, st)[r -- _length]) .intval → oktype(addarray(r0, ty0, i, st)[r -- j '], int_type, addarray(r0, ty0, i, st))) ↔ okarray(r, int_type, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ r ≠ r0 → (okreftype(refval(r), ty, addarray(r0, ty0, i, st)) ↔ okreftype(refval(r), ty, st))
Proof step 3:
⊦ r ≠ r0 → (r -- sk ∈ addarray(r0, ty, i, st) ↔ r -- sk ∈ st)
Proof step 4:
⊦ r ≠ r0 → (addarray(r, ty, i, st)[r0 -- sk]) = st[r0 -- sk]
Proof step 5:
⊦ r ≠ r0 → (is_arrayref(r, i, addarray(r0, ty0, i0, st)) ↔ is_arrayref(r, i, st))
Proof step 11:
⊦ r = r0, okreftype(refval(r), mkarraytype(int_type), st) ∧ r ≠ jvmref ∧ r -- _length ∈ st ∧ is_integervalue(st[r -- _length]) ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ (∀ j. ¬ j < 0 ∧ ¬ st[r -- _length] .intval ≤ j → is_integervalue(st[r -- j '])) ↔ okarray(r, int_type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ oktype(val, int_type, st) ↔ is_integervalue(val)], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i])]]