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Proof step 31 from proof okarray-subset (previous step)

st[r -- _length] = intval(st[r -- _length] .intval), st[r -- _type] = typeval(mkarraytype(ty0)), r ∈ st0, 0 ≤ st[r -- _length] .intval, r ∈ st, r -- _length ∈ st0, is_arrayref(r, st[r -- _length] .intval, st), r -- _length ∈ st, ty0 ≤ ty, r -- _type ∈ st, st ⊆ st0, ∀ j0. ¬ j0 < 0 ∧ ¬ st[r -- _length] .intval ≤ j0 → okval(st[r -- j0 '], ty) ⊦ r = jvmref, is_referencevalue(refval(r)) ∧ ( refval(r) .refval ≠ jvmref → refval(r) .refval -- _type ∈ st0 ∧ is_typevalue(st0[refval(r) .refval -- _type]) ∧ st0[refval(r) .refval -- _type] .type ≤ mkarraytype(ty)) ∧ is_arrayref(r, st[r -- _length] .intval, st0) ∧ (0 ≤ j ∧ j < st[r -- _length] .intval → okval(st0[r -- j '], ty))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 30:
st[r -- _length] = intval(st[r -- _length] .intval), st[r -- _type] = typeval(mkarraytype(ty0)), r ∈ st0, 0 ≤ st[r -- _length] .intval, r ∈ st, r -- _length ∈ st0, is_arrayref(r, st[r -- _length] .intval, st), r -- _length ∈ st, ty0 ≤ ty, r -- _type ∈ st, st ⊆ st0, r -- _type ∈ st0, ∀ j0. ¬ j0 < 0 ∧ ¬ st[r -- _length] .intval ≤ j0 → okval(st[r -- j0 '], ty) ⊦ r = jvmref, (0 ≤ j ∧ j < st[r -- _length] .intval → okval(st0[r -- j '], ty)) ∧ is_arrayref(r, st[r -- _length] .intval, st0) ∧ st0[r -- _type] .type ≤ mkarraytype(ty) ∧ is_typevalue(st0[r -- _type])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ rk ∈ st ∧ ¬ rk ∈ st0 → ¬ st ⊆ st0], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))])]]