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Proof step 52 from proof cyclic-addobj (previous step)

fis .keys = instfields(class), validrefs(str, r ' + refs0, mkclasstype(class), addobj(r, class, fis, st)), validfieldinits(fis, st), is_obj(str, r, addobj(r, class, fis, st)), newref(r, st), ∀ fs, r0. fs ' × refval(r0) ∈ fis → ¬ junkref(str, r0, st) ∧ ¬ cyclic(str, r0, st) ⊦ r = jvmref, ¬ r ∈ refs0 ∧ ¬ dups(refs0), ∃ fs. fs ' ∈ fis ∧ fs ' ∈ instfields(class) ∧ fis[fs '] = refval(r)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( validrefs(str, r ' + refs, ty, st) ↔ refs = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ refs .first = st[r -- fs '] .refval ∧ validrefs(str, refs, fs .type, st)))
Proof step 51:
is_obj(str, r, addobj(r, class, fis, st)) ∧ (addobj(r, class, fis, st)[r -- _type]) .type ≤ mkclasstype(class), fis .keys = instfields(class), refs0 = [] ∨ (∃ fs. fs ' ∈ instfields((addobj(r, class, fis, st)[r -- _type]) .type .class) ∧ is_referencevalue(addobj(r, class, fis, st)[r -- fs ']) ∧ refs0 .first = (addobj(r, class, fis, st)[r -- fs ']) .refval ∧ validrefs(str, refs0, fs .type, addobj(r, class, fis, st))), validfieldinits(fis, st), is_obj(str, r, addobj(r, class, fis, st)), newref(r, st), ∀ fs, r0. fs ' × refval(r0) ∈ fis → ¬ junkref(str, r0, st) ∧ ¬ cyclic(str, r0, st) ⊦ r = jvmref, ¬ r ∈ refs0 ∧ ¬ dups(refs0), ∃ fs. fs ' ∈ fis ∧ fs ' ∈ instfields(class) ∧ fis[fs '] = refval(r)

Rule argument

[crewrite-arg: validrefs-class , F , [st, ty, refs, r, str] → [addobj(r, class, fis, st), mkclasstype(class), refs0, r, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ fis .keys = instfields(class) → ¬ _type ∈ fis], [CSIMPSEQ : ¬ _type ∈ fis ⊦ (addobj(r, class1, fis, st) [r -- _type ] ) = typeval(mkclasstype(class1))], [CSIMPSEQ : ⊦ typeval(ty) .type = ty], [CSIMPSEQ : ⊦ mkclasstype(class1) ≤ mkclasstype(class2) ↔ class1 ≤ class2], [CSIMPSEQ : ⊦ class ≤ class])], [EXTRATERMS : (addobj(r, class, fis, st), mkclasstype(class), refs0, r, str)]]