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Proof step 131 from proof validref-refs-last-valid-subset (previous step)

acc + r1 ' = r2 ' + refs, st0[r0 -- mkfs(class, ty0, fieldvar) '] = refval(r2), st[r0 -- _type] = st0[r0 -- _type], is_obj(r0, st0), class+∃(str, st0[r0 -- _type] .type .class), validref(str, r0, st0[r0 -- _type] .type, st), st ⊆ st0, st0[r0 -- _type] .type ≤ ty, mkfs(class, ty0, fieldvar) ' ∈ instfields(st0[r0 -- _type] .type .class), validrefs(str, r2 ' + refs, ty0, 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, is_abstract(st0[r0 -- _type] .type .class), validref(str, r1, st[r1 -- _type] .type, st), r1 ≠ r2 ∧ ¬ r1 ∈ refs, ¬ r2 ∈ acc ∧ r2 ≠ r1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 91:
⊦ is_obj(r, st) ↔ r ≠ jvmref ∧ r -- _type ∈ st ∧ is_typevalue(st[r -- _type]) ∧ is_classtype(st[r -- _type] .type) ∧ is_obj(r, st[r -- _type] .type .class, st)
Proof step 130:
acc + r1 ' = r2 ' + refs, st0[r0 -- mkfs(class, ty0, fieldvar) '] = refval(r2), st[r0 -- _type] = st0[r0 -- _type], r0 ≠ jvmref ∧ r0 -- _type ∈ st0 ∧ is_typevalue(st0[r0 -- _type]) ∧ is_classtype(st0[r0 -- _type] .type) ∧ is_obj(r0, st0[r0 -- _type] .type .class, st0), class+∃(str, st0[r0 -- _type] .type .class), validref(str, r0, st0[r0 -- _type] .type, st), st ⊆ st0, st0[r0 -- _type] .type ≤ ty, mkfs(class, ty0, fieldvar) ' ∈ instfields(st0[r0 -- _type] .type .class), validrefs(str, r2 ' + refs, ty0, 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, is_abstract(st0[r0 -- _type] .type .class), validref(str, r1, st[r1 -- _type] .type, st), r1 ≠ r2 ∧ ¬ r1 ∈ refs, ¬ r2 ∈ acc ∧ r2 ≠ r1

Rule argument

[speclemmaarg: , is_obj(r, st) ↔ r ≠ jvmref ∧ r -- _type ∈ st ∧ is_typevalue(st[r -- _type]) ∧ is_classtype(st[r -- _type] .type) ∧ is_obj(r, st[r -- _type] .type .class, st) ,[st, r] → [st0, r0] ,F ,addfuns , ,is-any-object ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st0, r0)]]