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Proof step 7 from proof okarray (previous step)

⊦ ty = abstract_type, r = jvmref, okarray(r, ty, addarray(r, ty, i, st)) ↔ ¬ i < 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ 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 2:
⊦ okreftype(refval(r), mkarraytype(ty), addarray(r, ty, i, st))
Proof step 3:
⊦ r -- _length ∈ addarray(r, ty, i, st)
Proof step 4:
⊦ (addarray(r, ty, i, st)[r -- _length]) = intval(i)
Proof step 5:
⊦ is_arrayref(r, i, addarray(r, ty, i, st))
Proof step 6:
⊦ 0 ≤ j ∧ j < i → (addarray(r, ty, i, st)[r -- j ']) = initial_value(ty)

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, ty, i, st), ty, r] ,F ,okfuns , ,okarrayNotNull ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_integervalue(intval(i))], [CSIMPSEQ : ⊦ intval(i) .intval = i], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ oktype(initial_value(ty), ty, st) ↔ ty ≠ abstract_type])], [EXTRATERMS : (addarray(r, ty, i, st), ty, r)]]