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Proof step 11 from proof exactarray-in (previous step)

0 < st[r -- _length] .intval, exactreftype(refval(r), mkarraytype(ty), st) ∧ refval(r) .refval ≠ jvmref ∧ (refval(r) .refval -- _length) × intval(st[r -- _length] .intval) ∈ st ∧ is_arrayref(refval(r) .refval, st[r -- _length] .intval, st), i < st[r -- _length] .intval, 0 ≤ i ⊦ r = jvmref, r -- i ' ∈ st

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ exactreftype(val, ty, st) ↔ is_referencevalue(val) ∧ val .refval ∈ st ∧ (val .refval ≠ jvmref → val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type = ty)
Proof step 10:
st[r -- _type] .type = mkarraytype(ty), i < st[r -- _length] .intval, 0 ≤ i, 0 < st[r -- _length] .intval, r -- _type ∈ st, is_typevalue(st[r -- _type]), r -- _length ∈ st, is_arrayref(r, st[r -- _length] .intval, st), r ∈ st ⊦ r = jvmref, r -- i ' ∈ st

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ rk × val ∈ st ↔ rk ∈ st ∧ st[rk] = val], [CSIMPSEQ : is_integervalue(val) ⊦ intval(val .intval) = val], [CSIMPSEQ : ⊦ ¬ is_integervalue(val) → val .intval = 0], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ refval(r) .refval = r])]]