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Proof step 28 from proof okarray-onlymod (previous step)

st[r -- _length] = intval(st[r -- _length] .intval), st[r -- _type] = typeval(mkarraytype(ty0)), (∀ rk. rk ∈ st ↔ rk ∈ st0) ∧ (∀ r1, sk. r1 ≠ r0 → st[r1 -- sk] = st0[r1 -- sk]) ∧ (r0 -- _type ∈ st → st[r0 -- _type] = st0[r0 -- _type]) ∧ (r0 -- _length ∈ st → st[r0 -- _length] = st0[r0 -- _length]), r -- _type ∈ st, ty0 ≤ ty, r -- _length ∈ st, is_arrayref(r, st[r -- _length] .intval, st), is_arrayref(r, st[r -- _length] .intval, st0), r ∈ st, 0 ≤ st[r -- _length] .intval, ∀ j0. ¬ j0 < 0 ∧ ¬ st[r -- _length] .intval ≤ j0 → okval(st[r -- j0 '], ty) ⊦ r = r0, r = jvmref, r -- _type ∈ st0 ∧ is_typevalue(st0[r -- _type]) ∧ st0[r -- _type] .type ≤ mkarraytype(ty)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 27:
st[r -- _type] = typeval(mkarraytype(ty0)), st[r -- _length] = intval(st[r -- _length] .intval), 0 ≤ st[r -- _length] .intval, r ∈ st, is_arrayref(r, st[r -- _length] .intval, st0), is_arrayref(r, st[r -- _length] .intval, st), r -- _length ∈ st, ty0 ≤ ty, r -- _type ∈ st, ∀ j0. ¬ j0 < 0 ∧ ¬ st[r -- _length] .intval ≤ j0 → okval(st[r -- j0 '], ty), r0 -- _length ∈ st → st[r0 -- _length] = st0[r0 -- _length], r0 -- _type ∈ st → st[r0 -- _type] = st0[r0 -- _type], ∀ r1, sk. r1 ≠ r0 → st[r1 -- sk] = st0[r1 -- sk], ∀ rk. rk ∈ st ↔ rk ∈ st0 ⊦ r = jvmref, r = r0, r -- _type ∈ st0 ∧ is_typevalue(st0[r -- _type]) ∧ st0[r -- _type] .type ≤ mkarraytype(ty)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]