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Proof step 5 from proof isarray-add (previous step)

0 ≤ i ⊦ ty = abstract_type, r = jvmref, is_array(r, addarray(r, ty, i, st))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ is_array(r, st) ↔ r ≠ jvmref ∧ r -- _type ∈ st ∧ is_typevalue(st[r -- _type]) ∧ is_arraytype(st[r -- _type] .type) ∧ okarray(r, st[r -- _type] .type .type, st)
Proof step 2:
⊦ r -- _type ∈ addarray(r, ty, i, st)
Proof step 3:
⊦ (addarray(r, ty, i, st)[r -- _type]) = typeval(mkarraytype(ty))
Proof step 4:
⊦ r ≠ jvmref ∧ ty ≠ abstract_type → (okarray(r, ty, addarray(r, ty, i, st)) ↔ 0 ≤ i)

Rule argument

[speclemmaarg: , is_array(r, st) ↔ r ≠ jvmref ∧ r -- _type ∈ st ∧ is_typevalue(st[r -- _type]) ∧ is_arraytype(st[r -- _type] .type) ∧ okarray(r, st[r -- _type] .type .type, st) ,[st, r] → [addarray(r, ty, i, st), r] ,F ,okfuns , ,is-any-array ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_typevalue(typeval(ty))], [CSIMPSEQ : ⊦ typeval(ty) .type = ty], [CSIMPSEQ : ⊦ is_arraytype(mkarraytype(ty))], [CSIMPSEQ : ⊦ mkarraytype(ty) .type = ty], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])], [EXTRATERMS : (addarray(r, ty, i, st), r)]]