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Proof step 37 from proof validrefs-addobj-01 (previous step)

fis .keys = instfields(class), st[r0 -- _type] .type ≤ ty, is_valid_ref(str, r0, st), validref(str, r0, ty0, addobj(r, class, fis, st)), 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), validref(str, (addobj(r, class, fis, st)[r -- mkfs(class0, ty0, fieldvar) ']) .refval, ty0, addobj(r, class, fis, st)) ⊦ r0 = jvmref, r = jvmref, r0 = r, validrefs(str, r0 ' + refs0, ty0, addobj(r, class, fis, st)), is_abstract(class), validrefs(str, r0 ' + refs0, ty0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: ,sk ∈ fis → (addobj(r, class, fis, st)[r -- sk]) = fis[sk] ,[sk, st, fis, class, r] → [mkfs(class0, ty0, fieldvar) ', st, fis, class, r] ,F ,addfuns , ,add-in-09 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ sk × val ∈ fis → sk ∈ fis])], [EXTRATERMS : (mkfs(class0, ty0, fieldvar) ', st, fis, class, r)]]