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Proof step 40 from proof isarray-put-array-badindex (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 24:
r0 -- _length ∈ st[r -- i ', val] ∧ is_arrayref(r0, i0, st[r -- i ', val]) ∧ (∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → okval(st[r -- i ', val][r0 -- j '], ty)), st[r0 -- _type] = typeval(mkarraytype(ty)), st[r0 -- _length] = intval(i0), 0 ≤ i0, i < 0, r0 -- _type ∈ st, r0 ∈ st ⊦ okreftype(refval(r0), mkarraytype(ty), st) ∧ r0 -- _length ∈ st ∧ is_arrayref(r0, i0, st) ∧ (∀ j. 0 ≤ j ∧ j < i0 → okval(st[r0 -- j '], ty)), r0 = jvmref
Proof step 39:
okreftype(refval(r0), mkarraytype(ty), st) ∧ r0 -- _length ∈ st ∧ is_arrayref(r0, i0, st) ∧ (∀ j. 0 ≤ j ∧ j < i0 → okval(st[r0 -- j '], ty)), st[r0 -- _type] = typeval(mkarraytype(ty)), st[r0 -- _length] = intval(i0), 0 ≤ i0, i < 0, r0 -- _type ∈ st, r0 ∈ st ⊦ r0 -- _length ∈ st[r -- i ', val] ∧ is_arrayref(r0, i0, st[r -- i ', val]) ∧ (∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → okval(st[r -- i ', val][r0 -- j '], ty)), r0 = jvmref

Rule argument

[CASEDARG : pos: right 2, ()]

Additional information

[[CONCRETESIMPRULES : ()]]