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Proof step 12 from proof exactarray-lenin (previous step)

st[r -- _length] .intval = 141 * j0, i < j0, exactreftype(refval(r), mkarraytype(ty), st) ∧ r ≠ jvmref ∧ r -- _length ∈ st ∧ is_integervalue(st[r -- _length]) ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(r, st[r -- _length] .intval, st), 0 ≤ i, 0 < j0, r ∈ st ⊦ r = jvmref, r -- (i * 141) ' ∈ st

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ 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 11:
st[r -- _type] .type = mkarraytype(ty), st[r -- _length] .intval = 141 * j0, is_typevalue(st[r -- _type]), r -- _type ∈ st, i < j0, 0 < j0, 0 ≤ i, is_arrayref(r, 141 * j0, st), is_integervalue(st[r -- _length]), r -- _length ∈ st, r ∈ st, 0 ≤ j0 ⊦ r = jvmref, r -- (i * 141) ' ∈ st

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i * j = j * i], [CSIMPSEQ : ⊦ i * j * j0 = (i * j) * j0], [CSIMPSEQ : ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j)], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))])]]