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Proof step 42 from proof validrefs-primarray (previous step)

st[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(ty0)), 0 ≤ i, r ∈ st, is_primtype(ty), is_arrayref(r, i, st), r -- _length ∈ st, r -- _type ∈ st, ty0 ≤ ty, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r -- j '], ty) ⊦ r = jvmref, is_array(str, r, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 27:
⊦ ¬ is_reftype(ty0) → (ty ≤ ty0 ↔ ty = ty0)
Proof step 41:
¬ is_reftype(ty), st[r -- _length] = intval(i), st[r -- _type] = typeval(mkarraytype(ty0)), 0 ≤ i, r ∈ st, is_primtype(ty), is_arrayref(r, i, st), r -- _length ∈ st, r -- _type ∈ st, ty0 = ty, ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r -- j '], ty) ⊦ r = jvmref, is_array(str, r, st)

Rule argument

[speclemmaarg: ,¬ is_reftype(ty0) → (ty ≤ ty0 ↔ ty = ty0) ,[ty0, ty] → [ty, ty0] ,F ,typefuns , ,le-noreftype-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_reftype(ty) → ¬ is_primtype(ty)])], [EXTRATERMS : (ty, ty0)]]