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Proof step 18 from proof cyclic-addarray-this-01 (previous step)

vals[i→n(i)] = refval(r1), refval(r1) ∈ vals, validrefs(str, r1 ' + refs, ty, addarray(r0, ty, vals, st)), 0 ≤ i, is_array(str, r0, addarray(r0, ty, vals, st)), newref(r0, st), i < n→i(# vals), ∀ r. refval(r) ∈ vals → ¬ junkref(str, r, st) ∧ ¬ cyclic(str, r, st) ⊦ vals = [], r0 = jvmref, r0 = r1, cyclic(str, r1, st), junkref(str, r1, st), ¬ dups(refs) ∧ ¬ r1 ∈ refs ∧ ¬ r0 ∈ refs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ ¬ validrefs(str, refs, ty, st) ∧ newref(r, st) ∧ ¬ r ∈ refs → ¬ validrefs(str, refs, ty, addarray(r, ty0, vals, st))
Proof step 17:
¬ (¬ validrefs(str, r1 ' + refs, ty, st) ∧ newref(r0, st) ∧ ¬ r0 ∈ r1 ' + refs), vals[i→n(i)] = refval(r1), refval(r1) ∈ vals, validrefs(str, r1 ' + refs, ty, addarray(r0, ty, vals, st)), 0 ≤ i, is_array(str, r0, addarray(r0, ty, vals, st)), newref(r0, st), i < n→i(# vals), ∀ r. refval(r) ∈ vals → ¬ junkref(str, r, st) ∧ ¬ cyclic(str, r, st) ⊦ vals = [], r0 = jvmref, r0 = r1, cyclic(str, r1, st), junkref(str, r1, st), ¬ dups(refs) ∧ ¬ r1 ∈ refs ∧ ¬ r0 ∈ refs

Rule argument

[crewrite-arg: validrefs-addarray , F , [st, vals, ty0, r, ty, refs, str] → [st, vals, ty, r0, ty, r1 ' + refs, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, vals, ty, r0, ty, r1 ' + refs, str)]]