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Proof step 23 from proof junkref-addarray-01 (previous step)

newref(r, st), class∃(str, class), junkrefs(str, r ' + refs0, mkarraytype(mkclasstype(class)), addarray(r, mkclasstype(class), vals, st)), tdname+∃(str, class), ∀ val. val ∈ vals → ¬ junkref(str, val .refval, st) ∧ is_referencevalue(val) ∧ (val .refval ≠ jvmref → st[val .refval -- _type] .type ≤ mkclasstype(class)) ⊦ r = jvmref, okarray(r, mkclasstype(class), addarray(r, mkclasstype(class), vals, st))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ okarray(r, ty, st) ↔ okreftype(refval(r), mkarraytype(ty), st) ∧ r ≠ jvmref ∧ r -- _length ∈ st ∧ is_integervalue(st[r -- _length]) ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r -- _length] .intval → oktype(st[r -- j '], ty, st))
Proof step 22:
newref(r, st), class∃(str, class), junkrefs(str, r ' + refs0, mkarraytype(mkclasstype(class)), addarray(r, mkclasstype(class), vals, st)), tdname+∃(str, class), ∀ val. val ∈ vals → ¬ junkref(str, val .refval, st) ∧ is_referencevalue(val) ∧ (val .refval ≠ jvmref → st[val .refval -- _type] .type ≤ mkclasstype(class)) ⊦ r = jvmref, okreftype(refval(r), mkarraytype(mkclasstype(class)), addarray(r, mkclasstype(class), vals, st)) ∧ r ≠ jvmref ∧ r -- _length ∈ addarray(r, mkclasstype(class), vals, st) ∧ is_integervalue(addarray(r, mkclasstype(class), vals, st)[r -- _length]) ∧ 0 ≤ (addarray(r, mkclasstype(class), vals, st)[r -- _length]) .intval ∧ is_arrayref(r, (addarray(r, mkclasstype(class), vals, st)[r -- _length]) .intval, addarray(r, mkclasstype(class), vals, st)) ∧ (∀ j. 0 ≤ j ∧ j < (addarray(r, mkclasstype(class), vals, st)[r -- _length]) .intval → oktype(addarray(r, mkclasstype(class), vals, st)[r -- j '], mkclasstype(class), addarray(r, mkclasstype(class), vals, st)))

Rule argument

[speclemmaarg: , okarray(r, ty, st) ↔ okreftype(refval(r), mkarraytype(ty), st) ∧ r ≠ jvmref ∧ r -- _length ∈ st ∧ is_integervalue(st[r -- _length]) ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r -- _length] .intval → oktype(st[r -- j '], ty, st)) ,[st, ty, r] → [addarray(r, mkclasstype(class), vals, st), mkclasstype(class), r] ,F ,okfuns , ,okarrayNotNull ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (addarray(r, mkclasstype(class), vals, st), mkclasstype(class), r)]]