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Proof step 66 from proof cyclic-addobj (previous step)

fis[mkfs(class0, ty, fieldvar) '] = refval(r), fis .keys = instfields(class), mkfs(class0, ty, fieldvar) ' ∈ fis, mkfs(class0, ty, fieldvar) ' ∈ instfields(class), newref(r, st), is_obj(str, r, addobj(r, class, fis, st)), validfieldinits(fis, st), ∀ fs, r0. fs ' × refval(r0) ∈ fis → ¬ junkref(str, r0, st) ∧ ¬ cyclic(str, r0, st) ⊦ r = jvmref, validrefs(str, r ', ty, addobj(r, class, fis, st))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 63:
⊦ validrefs(str, r ', ty, st) ↔ r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, st) ∧ st[r -- _type] .type ≤ ty
Proof step 65:
fis[mkfs(class0, ty, fieldvar) '] = refval(r), fis .keys = instfields(class), mkfs(class0, ty, fieldvar) ' ∈ fis, mkfs(class0, ty, fieldvar) ' ∈ instfields(class), newref(r, st), is_obj(str, r, addobj(r, class, fis, st)), validfieldinits(fis, st), ∀ fs, r0. fs ' × refval(r0) ∈ fis → ¬ junkref(str, r0, st) ∧ ¬ cyclic(str, r0, st) ⊦ r = jvmref, r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, addobj(r, class, fis, st)) ∧ (addobj(r, class, fis, st)[r -- _type]) .type ≤ ty

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (addobj(r, class, fis, st), ty, r, str)]]