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Proof step 20 from proof cyclic-addobj (previous step)

fis[mkfs(class0, ty, fieldvar) '] = refval(r1), fis .keys = instfields(class), st[r1 -- _type] = typeval(ty0), 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, r ∈ refs, junkref(str, r1, st), cyclic(str, r1, st), ¬ dups(refs) ∧ ¬ r1 ∈ refs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ ¬ validrefs(str, refs, ty, st) ∧ ¬ r ∈ refs → ¬ validrefs(str, refs, ty, addobj(r, class, fis, st))
Proof step 19:
¬ (¬ validrefs(str, r1 ' + refs, ty, st) ∧ ¬ r ∈ r1 ' + refs), fis[mkfs(class0, ty, fieldvar) '] = refval(r1), fis .keys = instfields(class), st[r1 -- _type] = typeval(ty0), 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, r ∈ refs, junkref(str, r1, st), cyclic(str, r1, st), ¬ dups(refs) ∧ ¬ r1 ∈ refs

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, fis, class, r, ty, r1 ' + refs, str)]]