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Proof step 118 from proof validref-refs-last-valid-subset (previous step)

st0[r0 -- _type] = typeval(mkclasstype(class0)), st[r0 -- _type] = typeval(mkclasstype(class0)), st0[r0 -- mkfs(class, ty0, fieldvar) '] = refval(r2), acc + r1 ' = r2 ' + refs, st ⊆ st0, validref(str, r0, mkclasstype(class0), st), class+∃(str, class0), r0 -- _type ∈ st0, r0 ∈ st0, validrefs(str, r2 ' + refs, ty0, st0), mkfs(class, ty0, fieldvar) ' ∈ instfields(class0), class0 ≤ class1, r0 -- mkfs(class, ty0, fieldvar) ' ∈ st0, okval(refval(r2), ty0), ∀ sk. sk ∈ instfields(class0) → goodfieldandtype(r0, sk, st0), ∀ str, r, st, st0, r1, ty. validref(str, r, st[r -- _type] .type, st) ∧ st ⊆ st0 ∧ r ∈ acc ∧ validrefs(str, acc + r1 ', ty, st0) → validref(str, r1, st[r1 -- _type] .type, st) ⊦ r0 = jvmref, validref(str, r1, st[r1 -- _type] .type, st), is_abstract(class0), ¬ r2 ∈ acc ∧ r2 ≠ r1, r1 ≠ r2 ∧ ¬ r1 ∈ refs, ¬ validref(str, st[r0 -- mkfs(class, ty0, fieldvar) '] .refval, ty0, st) ∧ is_reftype(ty0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 95:
⊦ is_reftype(ty) → (okval(val, ty) ↔ is_referencevalue(val))
Proof step 117:
is_reftype(ty0), st0[r0 -- _type] = typeval(mkclasstype(class0)), st[r0 -- _type] = typeval(mkclasstype(class0)), st0[r0 -- mkfs(class, ty0, fieldvar) '] = refval(r2), acc + r1 ' = r2 ' + refs, st ⊆ st0, validref(str, r0, mkclasstype(class0), st), class+∃(str, class0), r0 -- _type ∈ st0, r0 ∈ st0, validrefs(str, r2 ' + refs, ty0, st0), mkfs(class, ty0, fieldvar) ' ∈ instfields(class0), class0 ≤ class1, r0 -- mkfs(class, ty0, fieldvar) ' ∈ st0, is_referencevalue(refval(r2)), ∀ sk. sk ∈ instfields(class0) → goodfieldandtype(r0, sk, st0), ∀ str, r, st, st0, r1, ty. validref(str, r, st[r -- _type] .type, st) ∧ st ⊆ st0 ∧ r ∈ acc ∧ validrefs(str, acc + r1 ', ty, st0) → validref(str, r1, st[r1 -- _type] .type, st) ⊦ r0 = jvmref, validref(str, r1, st[r1 -- _type] .type, st), is_abstract(class0), ¬ r2 ∈ acc ∧ r2 ≠ r1, r1 ≠ r2 ∧ ¬ r1 ∈ refs, ¬ validref(str, st[r0 -- mkfs(class, ty0, fieldvar) '] .refval, ty0, st) ∧ is_reftype(ty0)

Rule argument

[speclemmaarg: ,is_reftype(ty) → (okval(val, ty) ↔ is_referencevalue(val)) ,[ty, val] → [ty0, refval(r2)] ,F ,valuefuns , ,okval-reftype ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ okval(refval(r), ty) ↔ ty = void_type ∨ is_reftype(ty)], [CSIMPSEQ : ⊦ ¬ mkfs (class0, void_type, fieldvar) ' ∈ instfields(class)])], [EXTRATERMS : (ty0, refval(r2))]]