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Proof step 68 from proof okarray-union-03 (previous step)

okarray(refval(r), ty, st[r -- _length] .intval, st) ⊦ r = jvmref, (0 ≤ j ∧ j < st[r -- _length] .intval → oktype((st0 ∪ st)[r -- j '], ty, st0 ∪ st)) ∧ is_arrayref(r, st[r -- _length] .intval, st0 ∪ st) ∧ ¬ st[r -- _length] .intval < 0 ∧ (st0 ∪ st)[r -- _length] = intval(st[r -- _length] .intval) ∧ (r -- _length ∈ st0 ∨ r -- _length ∈ st) ∧ okreftype(refval(r), mkarraytype(ty), st0 ∪ st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ rk ∈ st0 → (st ∪ st0)[rk] = st0[rk]
Proof step 10:
¬ r -- _length ∈ st, okarray(refval(r), ty, st[r -- _length] .intval, st) ⊦ r = jvmref, (0 ≤ j ∧ j < st[r -- _length] .intval → oktype((st0 ∪ st)[r -- j '], ty, st0 ∪ st)) ∧ is_arrayref(r, st[r -- _length] .intval, st0 ∪ st) ∧ ¬ st[r -- _length] .intval < 0 ∧ (st0 ∪ st)[r -- _length] = intval(st[r -- _length] .intval) ∧ (r -- _length ∈ st0 ∨ r -- _length ∈ st) ∧ okreftype(refval(r), mkarraytype(ty), st0 ∪ st)
Proof step 67:
r -- _length ∈ st, okarray(refval(r), ty, st[r -- _length] .intval, st) ⊦ r = jvmref, (0 ≤ j ∧ j < st[r -- _length] .intval → oktype((st0 ∪ st)[r -- j '], ty, st0 ∪ st)) ∧ is_arrayref(r, st[r -- _length] .intval, st0 ∪ st) ∧ ¬ st[r -- _length] .intval < 0 ∧ st[r -- _length] = intval(st[r -- _length] .intval) ∧ (r -- _length ∈ st0 ∨ r -- _length ∈ st) ∧ okreftype(refval(r), mkarraytype(ty), st0 ∪ st)

Rule argument

[speclemmaarg: ,rk ∈ st0 → (st ∪ st0)[rk] = st0[rk] ,[rk, st0, st] → [r -- _length, st, st0] ,F ,storefunsx , ,union-at-right-01 ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (r -- _length, st, st0)]]