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Proof step 23 from proof isarray-put-array-badindex (previous step)

st[r0 -- _type] = typeval(mkarraytype(ty)), st[r0 -- _length] = intval(i0), r0 -- _length ∈ st[r -- i ', val], is_arrayref(r0, i0, st[r -- i ', val]), 0 ≤ i0, i < 0, r0 -- _type ∈ st, r0 ∈ st, r0 -- _length ∈ st, r0 ∈ st[r -- i ', val], ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → okval(st[r -- i ', val][r0 -- j '], ty) ⊦ r0 = jvmref, (0 ≤ j ∧ j < i0 → okval(st[r0 -- j '], ty)) ∧ is_arrayref(r0, i0, st) ∧ okreftype(refval(r0), mkarraytype(ty), st)

User applied rule case distinction

And obtained the following new goals

Proof step 13:
st[r0 -- _type] = typeval(mkarraytype(ty)), st[r0 -- _length] = intval(i0), r0 -- _length ∈ st[r -- i ', val], is_arrayref(r0, i0, st[r -- i ', val]), 0 ≤ i0, i < 0, r0 -- _type ∈ st, r0 ∈ st, r0 -- _length ∈ st, r0 ∈ st[r -- i ', val], ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → okval(st[r -- i ', val][r0 -- j '], ty) ⊦ 0 ≤ j ∧ j < i0 → okval(st[r0 -- j '], ty), r0 = jvmref
Proof step 20:
st[r0 -- _type] = typeval(mkarraytype(ty)), st[r0 -- _length] = intval(i0), r0 -- _length ∈ st[r -- i ', val], is_arrayref(r0, i0, st[r -- i ', val]), 0 ≤ i0, i < 0, r0 -- _type ∈ st, r0 ∈ st, r0 -- _length ∈ st, r0 ∈ st[r -- i ', val], ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → okval(st[r -- i ', val][r0 -- j '], ty) ⊦ is_arrayref(r0, i0, st), r0 = jvmref
Proof step 22:
st[r0 -- _type] = typeval(mkarraytype(ty)), st[r0 -- _length] = intval(i0), r0 -- _length ∈ st[r -- i ', val], is_arrayref(r0, i0, st[r -- i ', val]), 0 ≤ i0, i < 0, r0 -- _type ∈ st, r0 ∈ st, r0 -- _length ∈ st, r0 ∈ st[r -- i ', val], ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → okval(st[r -- i ', val][r0 -- j '], ty) ⊦ okreftype(refval(r0), mkarraytype(ty), st), r0 = jvmref

Rule argument

[CASEDARG : pos: right 2, ()]

Additional information

[[CONCRETESIMPRULES : ()]]