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Proof step 178 from proof exvalidrefs-maxlength (previous step)

st[r0 -- _type] .type = mkarraytype(ty), st[r0 -- 0 '] = refval(r0), ty .jtelemtype = mkclasstype(`java.lang.Object' .class), 0 < st[r0 -- _length] .intval, junkrefs(str, r0 ' + refs0, (st -- r0)[r0 -- _type] .type, st -- r0), mkarraytype(ty) ≤ ty, is_array(r0, st), is_array(str, r0, st), is_reftype(ty), ∀ r, str, st0. # st0 .refs < # st .refs → ( true → cyclic(str, r, st0) ∨ junkref(str, r, st0) ∨ (∃ refs. validrefs(str, refs, st0[refs .first -- _type] .type, st0) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r ∧ ¬ has_reffield(refs .last, st0))) ⊦ r0 = jvmref, ty = void_type, junkref(str, r0, st), validrefs(str, r0 ', ty, st), ∃ refs. validrefs(str, refs, st[refs .first -- _type] .type, st) ∧ refs ≠ [] ∧ ¬ dups(refs) ∧ refs .first = r0 ∧ ¬ has_reffield(refs .last, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 177:
⊦ validrefs(str, r ', ty, st) ↔ r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, st) ∧ st[r -- _type] .type ≤ ty

Rule argument

[crewrite-arg: validrefs-one, F, [st, ty, r, str] → [st, ty, r0, str]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ st[r -- _type] .type = mkarraytype(ty) ∧ r ≠ jvmref → ( is_valid_ref(str, r, st) ↔ is_array(str, r, st))])], [EXTRATERMS : (st, ty, r0, str)]]