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Proof step 15 from proof ac-okarray (previous step)

st[r -- _length] = intval(i), is_arrayref(r, i, st), 0 ≤ i ⊦ r = jvmref, r -- _type ∈ addclass(class1, fis, st) ∧ is_typevalue(st[r -- _type]) ∧ is_arraytype(st[r -- _type] .type) ∧ st[r -- _type] .type .type ≤ ty ∧ r -- _length ∈ addclass(class1, fis, st) ∧ (∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st[r -- j '], ty, st)) ↔ is_referencevalue(refval(r)) ∧ ( refval(r) .refval ≠ jvmref → refval(r) .refval -- _type ∈ st ∧ is_typevalue(st[refval(r) .refval -- _type]) ∧ st[refval(r) .refval -- _type] .type ≤ mkarraytype(ty)) ∧ r -- _length ∈ st ∧ (∀ j. 0 ≤ j ∧ j < i → oktype(st[r -- j '], ty, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
⊦ rk ∈ st → rk ∈ addclass(class, fis, st)
Proof step 14:
st[r -- _length] = intval(i), is_arrayref(r, i, st), 0 ≤ i, is_typevalue(st[r -- _type]), is_arraytype(st[r -- _type] .type), st[r -- _type] .type .type ≤ ty, j < i, r -- _length ∈ st, r -- _type ∈ st, 0 ≤ j, 0 < i, r ∈ st, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → oktype(st[r -- j '], ty, st) ⊦ r = jvmref, oktype(st[r -- j '], ty, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ intval(i) ≠ noval], [CSIMPSEQ : ⊦ ¬ is_typevalue(noval)], [CSIMPSEQ : ⊦ ∅[rk] = noval], [CSIMPSEQ : ⊦ ¬ rk ∈ st → st[rk] = ∅[rk]], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ ty0 ≤ mkarraytype(ty) ↔ is_arraytype(ty0) ∧ ty0 .type ≤ ty], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))])]]