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Proof step 13 from proof validrefs-primarray (previous step)

st[r -- _type] .type = mkarraytype(ty0), st[r -- i '] = refval(r0), validrefs(str, r0 ' + refs, ty0, st), r ∈ st, 0 ≤ i, 0 < st[r -- _length] .intval, is_primtype(ty), is_array(str, r, st), ty0 ≤ ty, okarray(r, ty, st), i < st[r -- _length] .intval ⊦ r ' + r0 ' + refs = jvmref ', r = jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ ¬ is_reftype(ty0) → (ty ≤ ty0 ↔ ty = ty0)
Proof step 12:
¬ is_reftype(ty), st[r -- _type] .type = mkarraytype(ty0), st[r -- i '] = refval(r0), validrefs(str, r0 ' + refs, ty0, st), r ∈ st, 0 ≤ i, 0 < st[r -- _length] .intval, is_primtype(ty), is_array(str, r, st), ty0 = ty, okarray(r, ty, st), i < st[r -- _length] .intval ⊦ r ' + r0 ' + refs = jvmref ', r = jvmref

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)]]