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Proof step 78 from proof validrefs-addobj-01 (previous step)

fis .keys = instfields(class), validrefs(str, r0 ' + refs0, ty, st), mkfs(class0, ty0, fieldvar) ' ∈ instfields(class), mkfs(class0, ty0, fieldvar) ' × refval(r0) ∈ fis, validref(str, r, mkclasstype(class), addobj(r, class, fis, st)), class+∃(str, class), newref(r, st), validFields(r, fis, addobj(r, class, fis, st)), is_obj(str, r, addobj(r, class, fis, st)), unique_al(fis) ⊦ r = jvmref, r0 ' + refs0 = jvmref ', is_abstract(class), is_reftype(ty0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 55:
⊦ r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty) → ¬ validref(str, r, ty, st)
Proof step 77:
¬ (r ≠ jvmref ∧ (¬ is_valid_ref(str, r, addobj(r, class, fis, st)) ∨ ¬ (addobj(r, class, fis, st)[r -- _type]) .type ≤ mkclasstype(class))), fis .keys = instfields(class), validrefs(str, r0 ' + refs0, ty, st), mkfs(class0, ty0, fieldvar) ' ∈ instfields(class), mkfs(class0, ty0, fieldvar) ' × refval(r0) ∈ fis, validref(str, r, mkclasstype(class), addobj(r, class, fis, st)), class+∃(str, class), newref(r, st), validFields(r, fis, addobj(r, class, fis, st)), is_obj(str, r, addobj(r, class, fis, st)), unique_al(fis) ⊦ r = jvmref, r0 ' + refs0 = jvmref ', is_abstract(class), is_reftype(ty0)

Rule argument

[speclemmaarg: , r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty) → ¬ validref(str, r, ty, st) ,[st, ty, r, str] → [addobj(r, class, fis, st), mkclasstype(class), r, str] ,F ,junkrefs , ,validref-is-junk ]

Additional information

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