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Proof step 16 from proof cyclic-addrefarray (previous step)

vals[i→n(i)] = refval(r0), refval(r0) ∈ vals, i < n→i(# vals), is_array(str, r, addarray(r, ty, vals, st)), is_reftype(ty), type∃(str, ty), newref(r, st), 0 ≤ i, validrefs(str, r0 ' + refs, ty, addarray(r, ty, vals, st)), st[r0 -- _type] .type ≤ ty, ∀ val. val ∈ vals → ¬ junkref(str, val .refval, st) ∧ ¬ cyclic(str, val .refval, st) ∧ is_referencevalue(val) ∧ (val .refval ≠ jvmref → st[val .refval -- _type] .type ≤ ty) ⊦ r = jvmref, ty .jtelemtype = void_type, ty .jtelemtype = abstract_type, vals = [], r = r0, r0 = jvmref, cyclic(str, r0, st), junkref(str, r0, st), ¬ dups(refs) ∧ ¬ r0 ∈ refs ∧ ¬ r ∈ refs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ validrefs(str, refs, ty0, addarray(r, ty, vals, st)) ∧ newref(r, st) ∧ r ∈ refs ∧ r0 = refs .first → junkref(str, r0, st)
Proof step 15:
¬ (validrefs(str, r0 ' + refs, ty, addarray(r, ty, vals, st)) ∧ newref(r, st) ∧ r ∈ r0 ' + refs ∧ r0 = (r0 ' + refs) .first), vals[i→n(i)] = refval(r0), refval(r0) ∈ vals, i < n→i(# vals), is_array(str, r, addarray(r, ty, vals, st)), is_reftype(ty), type∃(str, ty), newref(r, st), 0 ≤ i, validrefs(str, r0 ' + refs, ty, addarray(r, ty, vals, st)), st[r0 -- _type] .type ≤ ty, ∀ val. val ∈ vals → ¬ junkref(str, val .refval, st) ∧ ¬ cyclic(str, val .refval, st) ∧ is_referencevalue(val) ∧ (val .refval ≠ jvmref → st[val .refval -- _type] .type ≤ ty) ⊦ r = jvmref, ty .jtelemtype = void_type, ty .jtelemtype = abstract_type, vals = [], r = r0, r0 = jvmref, cyclic(str, r0, st), junkref(str, r0, st), ¬ dups(refs) ∧ ¬ r0 ∈ refs ∧ ¬ r ∈ refs

Rule argument

[crewrite-arg: validrefs-addarray-junkref , F , [str, refs, ty0, r, ty, vals, st, r0] → [str, r0 ' + refs, ty, r, ty, vals, st, r0] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (str, r0 ' + refs, ty, r, ty, vals, st, r0)]]