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Proof step 41 from proof validrefs-addobj-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

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), ty0, r0, str] ,F ,junkrefs , ,validref-is-junk ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ≠ r0 → ( is_valid_ref (str, r, addobj(r0, class, fis, st)) ↔ is_valid_ref(str, r, st))], [CSIMPSEQ : ⊦ r ≠ r0 → (addobj(r, class1, fis, st) [r0 -- sk ] ) = st[r0 -- sk]], [CSIMPSEQ : ⊦ ¬ is_reftype(ty0) → (ty ≤ ty0 ↔ ty = ty0)], [CSIMPSEQ : ⊦ ¬ is_reftype(ty) → (ty ≤ ty0 ↔ ty = ty0)], [CSIMPSEQ : ⊦ ¬ is_reftype (st[r -- _type] .type) → ¬ is_valid_ref(str, r, st)])], [EXTRATERMS : (addobj(r, class, fis, st), ty0, r0, str)]]