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Proof step 10 from proof cyclic-addobj (previous step)

fis[mkfs(class0, ty, fieldvar) '] = refval(r1), fis .keys = instfields(class), st[r1 -- _type] = typeval(ty0), r ∈ refs, validrefs(str, r1 ' + refs, ty, addobj(r, class, fis, st)), mkfs(class0, ty, fieldvar) ' ∈ instfields(class), newref(r, st), is_obj(str, r, addobj(r, class, fis, st)), mkfs(class0, ty, fieldvar) ' ∈ fis, okval(refval(r1), ty), r1 -- _type ∈ st, ty0 ≤ ty, r1 ∈ st, ∀ fs, r0. fs ' × refval(r0) ∈ fis → ¬ junkref(str, r0, st) ∧ ¬ cyclic(str, r0, st) ⊦ r1 = jvmref, r = jvmref, junkref(str, r1, st), cyclic(str, r1, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ validrefs(str, refs, ty0, addobj(r, class, fis, st)) ∧ newref(r, st) ∧ r ∈ refs ∧ r0 = refs .first → junkref(str, r0, st)

Rule argument

[crewrite-arg: validrefs-addobj-junkref , F , [str, refs, ty0, r, class, fis, st, r0] → [str, r1 ' + refs, ty, r, class, fis, st, r1] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ r ∈ r0 ' + refs ↔ r ≠ r0 ∧ ¬ r ∈ refs], [CSIMPSEQ : ⊦ newref(r, st) ∧ r0 ∈ st ∧ r0 ≠ jvmref → r ≠ r0], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ (r ' + refs) .first = r])], [EXTRATERMS : (str, r1 ' + refs, ty, r, class, fis, st, r1)]]